Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself > Representation of fundamental system solutions near zero





http://functions.wolfram.com/07.28.13.0010.01









  


  










Input Form





Derivative[4][w][z] + ((1/(-1 + a r^z)) (3 Log[r] - 4 (-1 + a r^z) Log[s] + a r^z Log[r] (Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4]) - Log[r] (Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3]))) Derivative[3][w][z] + (1/(-1 + a r^z)) (-3 (Log[r]^2 + 3 Log[r] Log[s] - 2 (-1 + a r^z) Log[s]^2) + a r^z Log[r] Subscript[a, 2] (-3 Log[s] + Log[r] (Subscript[a, 3] + Subscript[a, 4])) + a r^z Log[r] Subscript[a, 1] (-3 Log[s] + Log[r] (Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4])) + Log[r] (-3 a r^z Log[s] Subscript[a, 4] - a r^z Subscript[a, 3] (3 Log[s] - Log[r] Subscript[a, 4]) + (2 Log[r] + 3 Log[s]) Subscript[b, 3] + Subscript[b, 2] (2 Log[r] + 3 Log[s] - Log[r] Subscript[b, 3]) - Subscript[b, 1] (-2 Log[r] - 3 Log[s] + Log[r] (Subscript[b, 2] + Subscript[b, 3])))) Derivative[2][w][z] + (1/(-1 + a r^z)) (-4 a r^z Log[s]^3 + (Log[r] + Log[s])^2 (Log[r] + 4 Log[s]) + a r^z Log[r] Subscript[a, 2] (Log[s] (3 Log[s] - 2 Log[r] Subscript[a, 4]) + Log[r] Subscript[a, 3] (-2 Log[s] + Log[r] Subscript[a, 4])) + a r^z Log[r] Subscript[a, 1] (3 Log[s]^2 + Log[r] (-2 Log[s] Subscript[a, 4] + Subscript[a, 3] (-2 Log[s] + Log[r] Subscript[a, 4]) + Subscript[a, 2] (-2 Log[s] + Log[r] (Subscript[a, 3] + Subscript[a, 4])))) - Log[r] (-3 a r^z Log[s]^2 Subscript[a, 4] - a r^z Log[s] Subscript[a, 3] (3 Log[s] - 2 Log[r] Subscript[a, 4]) + (Log[r] + Log[s]) (Log[r] + 3 Log[s]) Subscript[b, 3] + Subscript[b, 2] ((Log[r] + Log[s]) (Log[r] + 3 Log[s]) - Log[r] (Log[r] + 2 Log[s]) Subscript[b, 3]) + Subscript[b, 1] ((Log[r] + Log[s]) (Log[r] + 3 Log[s]) + Log[r] ((-(Log[r] + 2 Log[s])) Subscript[b, 3] + Subscript[b, 2] (-Log[r] - 2 Log[s] + Log[r] Subscript[b, 3]))))) Derivative[1][w][z] + (1/(-1 + a r^z)) (a r^z (Log[s] - Log[r] Subscript[a, 1]) (Log[s] - Log[r] Subscript[a, 2]) (Log[s] - Log[r] Subscript[a, 3]) (Log[s] - Log[r] Subscript[a, 4]) - Log[s] (Log[r] + Log[s] - Log[r] Subscript[b, 1]) (Log[r] + Log[s] - Log[r] Subscript[b, 2]) (Log[r] + Log[s] - Log[r] Subscript[b, 3])) w[z] == 0 /; w[z] == Subscript[c, 1] s^z HypergeometricPFQRegularized[ {Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, a z^r] + Subscript[c, 2] s^z (MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3], 1 - Subscript[a, 4]}, {}}, {{0, 1 - Subscript[b, 1]}, {1 - Subscript[b, 2], 1 - Subscript[b, 3]}}, a r^z] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3], 1 - Subscript[a, 4]}, {}}, {{0, 1 - Subscript[b, 2]}, {1 - Subscript[b, 1], 1 - Subscript[b, 3]}}, a r^z] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3], 1 - Subscript[a, 4]}, {}}, {{0, 1 - Subscript[b, 3]}, {1 - Subscript[b, 1], 1 - Subscript[b, 2]}}, a r^z]) + Subscript[c, 3] s^z (MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3], 1 - Subscript[a, 4]}, {}}, {{0, 1 - Subscript[b, 1], 1 - Subscript[b, 2]}, {1 - Subscript[b, 3]}}, (-a) r^z] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3], 1 - Subscript[a, 4]}, {}}, {{0, 1 - Subscript[b, 1], 1 - Subscript[b, 3]}, {1 - Subscript[b, 2]}}, (-a) r^z] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3], 1 - Subscript[a, 4]}, {}}, {{0, 1 - Subscript[b, 2], 1 - Subscript[b, 3]}, {1 - Subscript[b, 1]}}, (-a) r^z]) + Subscript[c, 4] s^z MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3], 1 - Subscript[a, 4]}, {}}, {{0, 1 - Subscript[b, 1], 1 - Subscript[b, 2], 1 - Subscript[b, 3]}, {}}, a r^z]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "4", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z", "]"]], "+", RowBox[List[RowBox[List[FractionBox["1", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["3", " ", RowBox[List["Log", "[", "r", "]"]]]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], ")"]], " ", RowBox[List["Log", "[", "s", "]"]]]], "+", RowBox[List["a", " ", SuperscriptBox["r", "z"], " ", RowBox[List["Log", "[", "r", "]"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["a", "1"], "+", SubscriptBox["a", "2"], "+", SubscriptBox["a", "3"], "+", SubscriptBox["a", "4"]]], ")"]]]], "-", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["b", "1"], "+", SubscriptBox["b", "2"], "+", SubscriptBox["b", "3"]]], ")"]]]]]], ")"]]]], " ", RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "3", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z", "]"]]]], "+", RowBox[List[FractionBox["1", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["Log", "[", "r", "]"]], "2"], "+", RowBox[List["3", " ", RowBox[List["Log", "[", "r", "]"]], " ", RowBox[List["Log", "[", "s", "]"]]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Log", "[", "s", "]"]], "2"]]]]], ")"]]]], "+", RowBox[List["a", " ", SuperscriptBox["r", "z"], " ", RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", RowBox[List["Log", "[", "s", "]"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["a", "3"], "+", SubscriptBox["a", "4"]]], ")"]]]]]], ")"]]]], "+", RowBox[List["a", " ", SuperscriptBox["r", "z"], " ", RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["a", "1"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", RowBox[List["Log", "[", "s", "]"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["a", "2"], "+", SubscriptBox["a", "3"], "+", SubscriptBox["a", "4"]]], ")"]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", "a", " ", SuperscriptBox["r", "z"], " ", RowBox[List["Log", "[", "s", "]"]], " ", SubscriptBox["a", "4"]]], "-", RowBox[List["a", " ", SuperscriptBox["r", "z"], " ", SubscriptBox["a", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", RowBox[List["Log", "[", "s", "]"]]]], "-", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["a", "4"]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["Log", "[", "r", "]"]]]], "+", RowBox[List["3", " ", RowBox[List["Log", "[", "s", "]"]]]]]], ")"]], " ", SubscriptBox["b", "3"]]], "+", RowBox[List[SubscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["Log", "[", "r", "]"]]]], "+", RowBox[List["3", " ", RowBox[List["Log", "[", "s", "]"]]]], "-", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["b", "3"]]]]], ")"]]]], "-", RowBox[List[SubscriptBox["b", "1"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Log", "[", "r", "]"]]]], "-", RowBox[List["3", " ", RowBox[List["Log", "[", "s", "]"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["b", "2"], "+", SubscriptBox["b", "3"]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], "+", RowBox[List[FractionBox["1", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "a", " ", SuperscriptBox["r", "z"], " ", SuperscriptBox[RowBox[List["Log", "[", "s", "]"]], "3"]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r", "]"]], "+", RowBox[List["Log", "[", "s", "]"]]]], ")"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r", "]"]], "+", RowBox[List["4", " ", RowBox[List["Log", "[", "s", "]"]]]]]], ")"]]]], "+", RowBox[List["a", " ", SuperscriptBox["r", "z"], " ", RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Log", "[", "s", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", RowBox[List["Log", "[", "s", "]"]]]], "-", RowBox[List["2", " ", RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["a", "4"]]]]], ")"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["a", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Log", "[", "s", "]"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["a", "4"]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["a", " ", SuperscriptBox["r", "z"], " ", RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["a", "1"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox[RowBox[List["Log", "[", "s", "]"]], "2"]]], "+", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Log", "[", "s", "]"]], " ", SubscriptBox["a", "4"]]], "+", RowBox[List[SubscriptBox["a", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Log", "[", "s", "]"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["a", "4"]]]]], ")"]]]], "+", RowBox[List[SubscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Log", "[", "s", "]"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["a", "3"], "+", SubscriptBox["a", "4"]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", "a", " ", SuperscriptBox["r", "z"], " ", SuperscriptBox[RowBox[List["Log", "[", "s", "]"]], "2"], " ", SubscriptBox["a", "4"]]], "-", RowBox[List["a", " ", SuperscriptBox["r", "z"], " ", RowBox[List["Log", "[", "s", "]"]], " ", SubscriptBox["a", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", RowBox[List["Log", "[", "s", "]"]]]], "-", RowBox[List["2", " ", RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["a", "4"]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r", "]"]], "+", RowBox[List["Log", "[", "s", "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r", "]"]], "+", RowBox[List["3", " ", RowBox[List["Log", "[", "s", "]"]]]]]], ")"]], " ", SubscriptBox["b", "3"]]], "+", RowBox[List[SubscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r", "]"]], "+", RowBox[List["Log", "[", "s", "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r", "]"]], "+", RowBox[List["3", " ", RowBox[List["Log", "[", "s", "]"]]]]]], ")"]]]], "-", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r", "]"]], "+", RowBox[List["2", " ", RowBox[List["Log", "[", "s", "]"]]]]]], ")"]], " ", SubscriptBox["b", "3"]]]]], ")"]]]], "+", RowBox[List[SubscriptBox["b", "1"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r", "]"]], "+", RowBox[List["Log", "[", "s", "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r", "]"]], "+", RowBox[List["3", " ", RowBox[List["Log", "[", "s", "]"]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r", "]"]], "+", RowBox[List["2", " ", RowBox[List["Log", "[", "s", "]"]]]]]], ")"]]]], " ", SubscriptBox["b", "3"]]], "+", RowBox[List[SubscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", "r", "]"]]]], "-", RowBox[List["2", " ", RowBox[List["Log", "[", "s", "]"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["b", "3"]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], "+", RowBox[List[FractionBox["1", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["a", " ", SuperscriptBox["r", "z"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "s", "]"]], "-", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["a", "1"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "s", "]"]], "-", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["a", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "s", "]"]], "-", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["a", "3"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "s", "]"]], "-", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["a", "4"]]]]], ")"]]]], "-", RowBox[List[RowBox[List["Log", "[", "s", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r", "]"]], "+", RowBox[List["Log", "[", "s", "]"]], "-", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["b", "1"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r", "]"]], "+", RowBox[List["Log", "[", "s", "]"]], "-", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["b", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r", "]"]], "+", RowBox[List["Log", "[", "s", "]"]], "-", RowBox[List[RowBox[List["Log", "[", "r", "]"]], " ", SubscriptBox["b", "3"]]]]], ")"]]]]]], ")"]], " ", RowBox[List["w", "[", "z", "]"]]]]]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[SubscriptBox["c", "1"], SuperscriptBox["s", "z"], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", SubscriptBox["a", "2"], ",", SubscriptBox["a", "3"], ",", SubscriptBox["a", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"], ",", SubscriptBox["b", "3"]]], "}"]], ",", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "2"], " ", SuperscriptBox["s", "z"], RowBox[List["(", RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "3"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "4"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", SubscriptBox["b", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["b", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "3"]]]]], "}"]]]], "}"]], ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]], "+", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "3"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "4"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", SubscriptBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "3"]]]]], "}"]]]], "}"]], ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]], "+", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "3"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "4"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", SubscriptBox["b", "3"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "2"]]]]], "}"]]]], "}"]], ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]]]], ")"]]]], "+", RowBox[List[SubscriptBox["c", "3"], " ", SuperscriptBox["s", "z"], RowBox[List["(", RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "3"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "4"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "-", SubscriptBox["b", "3"]]], "}"]]]], "}"]], ",", RowBox[List[RowBox[List["-", "a"]], " ", SuperscriptBox["r", "z"]]]]], "]"]], "+", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "3"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "4"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "3"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "-", SubscriptBox["b", "2"]]], "}"]]]], "}"]], ",", RowBox[List[RowBox[List["-", "a"]], " ", SuperscriptBox["r", "z"]]]]], "]"]], "+", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "3"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "4"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", SubscriptBox["b", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "3"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "-", SubscriptBox["b", "1"]]], "}"]]]], "}"]], ",", RowBox[List[RowBox[List["-", "a"]], " ", SuperscriptBox["r", "z"]]]]], "]"]]]], ")"]]]], "+", RowBox[List[SubscriptBox["c", "4"], " ", SuperscriptBox["s", "z"], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "3"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "4"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "3"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]]]]]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mrow> <msup> <mi> w </mi> <semantics> <mrow> <mo> ( </mo> <mn> 4 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, &quot;4&quot;, &quot;)&quot;]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> w </mi> <semantics> <mrow> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, &quot;3&quot;, &quot;)&quot;]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> w </mi> <mi> &#8242;&#8242; </mi> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> w </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#63449; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mrow> <msub> <mi> c </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <msup> <mi> s </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 4 </mn> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mn> 3 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> , </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> <mo> ; </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> ; </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, &quot;4&quot;], SubscriptBox[OverscriptBox[&quot;F&quot;, &quot;~&quot;], &quot;3&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox[&quot;a&quot;, &quot;1&quot;], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;a&quot;, &quot;2&quot;], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;a&quot;, &quot;3&quot;], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;a&quot;, &quot;4&quot;], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[SubscriptBox[&quot;b&quot;, &quot;1&quot;], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;b&quot;, &quot;2&quot;], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;b&quot;, &quot;3&quot;], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[RowBox[List[&quot;a&quot;, &quot; &quot;, SuperscriptBox[&quot;z&quot;, &quot;r&quot;]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQRegularized] </annotation> </semantics> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <msub> <mi> c </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <msup> <mi> s </mi> <mi> z </mi> </msup> <mo> ( </mo> <mrow> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 4 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;4&quot;, &quot;,&quot;, &quot;4&quot;]], RowBox[List[&quot;2&quot;, &quot;,&quot;, &quot;4&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[RowBox[List[&quot;a&quot;, &quot; &quot;, SuperscriptBox[&quot;r&quot;, &quot;z&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;3&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;4&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;3&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mo> + </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 4 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;4&quot;, &quot;,&quot;, &quot;4&quot;]], RowBox[List[&quot;2&quot;, &quot;,&quot;, &quot;4&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[RowBox[List[&quot;a&quot;, &quot; &quot;, SuperscriptBox[&quot;r&quot;, &quot;z&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;3&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;4&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;3&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mo> + </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 4 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;4&quot;, &quot;,&quot;, &quot;4&quot;]], RowBox[List[&quot;2&quot;, &quot;,&quot;, &quot;4&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[RowBox[List[&quot;a&quot;, &quot; &quot;, SuperscriptBox[&quot;r&quot;, &quot;z&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;3&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;4&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;3&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> + </mo> <mtext> </mtext> <mrow> <msub> <mi> c </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <mrow> <msup> <mi> s </mi> <mi> z </mi> </msup> <mo> ( </mo> <mrow> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 4 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 3 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;4&quot;, &quot;,&quot;, &quot;4&quot;]], RowBox[List[&quot;3&quot;, &quot;,&quot;, &quot;4&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[RowBox[List[RowBox[List[&quot;-&quot;, &quot;a&quot;]], &quot; &quot;, SuperscriptBox[&quot;r&quot;, &quot;z&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;3&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;4&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;3&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mo> + </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 4 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 3 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;4&quot;, &quot;,&quot;, &quot;4&quot;]], RowBox[List[&quot;3&quot;, &quot;,&quot;, &quot;4&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[RowBox[List[RowBox[List[&quot;-&quot;, &quot;a&quot;]], &quot; &quot;, SuperscriptBox[&quot;r&quot;, &quot;z&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;3&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;4&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;3&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mo> + </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 4 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 3 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;4&quot;, &quot;,&quot;, &quot;4&quot;]], RowBox[List[&quot;3&quot;, &quot;,&quot;, &quot;4&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[RowBox[List[RowBox[List[&quot;-&quot;, &quot;a&quot;]], &quot; &quot;, SuperscriptBox[&quot;r&quot;, &quot;z&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;3&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;4&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;3&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mtext> </mtext> <mrow> <msub> <mi> c </mi> <mn> 4 </mn> </msub> <mo> &#8290; </mo> <msup> <mi> s </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 4 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 4 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;4&quot;, &quot;,&quot;, &quot;4&quot;]], RowBox[List[&quot;4&quot;, &quot;,&quot;, &quot;4&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[RowBox[List[&quot;a&quot;, &quot; &quot;, SuperscriptBox[&quot;r&quot;, &quot;z&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;3&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;4&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;3&quot;]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 4 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <ln /> <ci> r </ci> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ln /> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <ln /> <ci> s </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <ci> r </ci> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 3 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <ln /> <ci> r </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <ln /> <ci> r </ci> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ln /> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <ln /> <ci> r </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <ln /> <ci> r </ci> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ln /> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <plus /> <apply> <power /> <apply> <ln /> <ci> r </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ln /> <ci> s </ci> </apply> <apply> <ln /> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <ln /> <ci> s </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ln /> <ci> r </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -3 </cn> <ci> a </ci> <apply> <ln /> <ci> s </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ln /> <ci> s </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <ci> r </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ln /> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ln /> <ci> s </ci> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <ln /> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ln /> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ln /> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <ln /> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ln /> <ci> r </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ln /> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -4 </cn> <ci> a </ci> <apply> <power /> <apply> <ln /> <ci> s </ci> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <ln /> <ci> r </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <ln /> <ci> r </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <ln /> <ci> r </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ln /> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ln /> <ci> s </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ln /> <ci> s </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ln /> <ci> r </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <ln /> <ci> r </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <apply> <ln /> <ci> s </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <ln /> <ci> r </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <ln /> <ci> s </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <ln /> <ci> r </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ln /> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <ln /> <ci> r </ci> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ln /> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <ln /> <ci> r </ci> </apply> <apply> <ln /> <ci> s </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ln /> <ci> r </ci> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ln /> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <ci> r </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -3 </cn> <ci> a </ci> <apply> <power /> <apply> <ln /> <ci> s </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <ln /> <ci> s </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ln /> <ci> s </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ln /> <ci> r </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <ln /> <ci> r </ci> </apply> <apply> <ln /> <ci> s </ci> </apply> </apply> <apply> <plus /> <apply> <ln /> <ci> r </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ln /> <ci> s </ci> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <ln /> <ci> r </ci> </apply> <apply> <ln /> <ci> s </ci> </apply> </apply> <apply> <plus /> <apply> <ln /> <ci> r </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ln /> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <ci> r </ci> </apply> <apply> <plus /> <apply> <ln /> <ci> r </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ln /> <ci> s </ci> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <ln /> <ci> r </ci> </apply> <apply> <ln /> <ci> s </ci> </apply> </apply> <apply> <plus /> <apply> <ln /> <ci> r </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ln /> <ci> s </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ln /> <ci> r </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ln /> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ln /> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <ln /> <ci> r </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ln /> <ci> s </ci> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <ln /> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <ci> r </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <ln /> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <ci> r </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <ln /> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <ci> r </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <ln /> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <ci> r </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <ci> s </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ln /> <ci> r </ci> </apply> </apply> <apply> <ln /> <ci> r </ci> </apply> <apply> <ln /> <ci> s </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ln /> <ci> r </ci> </apply> </apply> <apply> <ln /> <ci> r </ci> </apply> <apply> <ln /> <ci> s </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <ln /> <ci> r </ci> </apply> </apply> <apply> <ln /> <ci> r </ci> </apply> <apply> <ln /> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> <apply> <ci> w </ci> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <ci> w </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> c </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <ci> s </ci> <ci> z </ci> </apply> <apply> <ci> HypergeometricPFQRegularized </ci> <list> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </list> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <apply> <power /> <ci> s </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <ci> MeijerG </ci> <list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </list> <list /> </list> <list> <list> <cn type='integer'> 0 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </list> </list> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> MeijerG </ci> <list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </list> <list /> </list> <list> <list> <cn type='integer'> 0 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </list> </list> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> MeijerG </ci> <list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </list> <list /> </list> <list> <list> <cn type='integer'> 0 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </list> </list> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> c </ci> <cn type='integer'> 3 </cn> </apply> <apply> <apply> <power /> <ci> s </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <ci> MeijerG </ci> <list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </list> <list /> </list> <list> <list> <cn type='integer'> 0 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </list> </list> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> MeijerG </ci> <list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </list> <list /> </list> <list> <list> <cn type='integer'> 0 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </list> </list> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> MeijerG </ci> <list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </list> <list /> </list> <list> <list> <cn type='integer'> 0 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </list> </list> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> c </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> s </ci> <ci> z </ci> </apply> <apply> <ci> MeijerG </ci> <list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </list> <list /> </list> <list> <list> <cn type='integer'> 0 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </list> <list /> </list> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "4", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z_", "]"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["3", " ", RowBox[List["Log", "[", "r_", "]"]]]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"]]]]], ")"]], " ", RowBox[List["Log", "[", "s_", "]"]]]], "+", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"], " ", RowBox[List["Log", "[", "r_", "]"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["a_", "1"], "+", SubscriptBox["a_", "2"], "+", SubscriptBox["a_", "3"], "+", SubscriptBox["a_", "4"]]], ")"]]]], "-", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["b_", "1"], "+", SubscriptBox["b_", "2"], "+", SubscriptBox["b_", "3"]]], ")"]]]]]], ")"]], " ", RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "3", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z_", "]"]]]], RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"]]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["Log", "[", "r_", "]"]], "2"], "+", RowBox[List["3", " ", RowBox[List["Log", "[", "r_", "]"]], " ", RowBox[List["Log", "[", "s_", "]"]]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Log", "[", "s_", "]"]], "2"]]]]], ")"]]]], "+", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"], " ", RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["a_", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", RowBox[List["Log", "[", "s_", "]"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["a_", "3"], "+", SubscriptBox["a_", "4"]]], ")"]]]]]], ")"]]]], "+", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"], " ", RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["a_", "1"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", RowBox[List["Log", "[", "s_", "]"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["a_", "2"], "+", SubscriptBox["a_", "3"], "+", SubscriptBox["a_", "4"]]], ")"]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", "a_", " ", SuperscriptBox["r_", "z_"], " ", RowBox[List["Log", "[", "s_", "]"]], " ", SubscriptBox["a_", "4"]]], "-", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"], " ", SubscriptBox["a_", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", RowBox[List["Log", "[", "s_", "]"]]]], "-", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["a_", "4"]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["Log", "[", "r_", "]"]]]], "+", RowBox[List["3", " ", RowBox[List["Log", "[", "s_", "]"]]]]]], ")"]], " ", SubscriptBox["b_", "3"]]], "+", RowBox[List[SubscriptBox["b_", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["Log", "[", "r_", "]"]]]], "+", RowBox[List["3", " ", RowBox[List["Log", "[", "s_", "]"]]]], "-", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["b_", "3"]]]]], ")"]]]], "-", RowBox[List[SubscriptBox["b_", "1"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Log", "[", "r_", "]"]]]], "-", RowBox[List["3", " ", RowBox[List["Log", "[", "s_", "]"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["b_", "2"], "+", SubscriptBox["b_", "3"]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"]]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "a_", " ", SuperscriptBox["r_", "z_"], " ", SuperscriptBox[RowBox[List["Log", "[", "s_", "]"]], "3"]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], "+", RowBox[List["Log", "[", "s_", "]"]]]], ")"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], "+", RowBox[List["4", " ", RowBox[List["Log", "[", "s_", "]"]]]]]], ")"]]]], "+", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"], " ", RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["a_", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Log", "[", "s_", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", RowBox[List["Log", "[", "s_", "]"]]]], "-", RowBox[List["2", " ", RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["a_", "4"]]]]], ")"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["a_", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Log", "[", "s_", "]"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["a_", "4"]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"], " ", RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["a_", "1"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox[RowBox[List["Log", "[", "s_", "]"]], "2"]]], "+", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Log", "[", "s_", "]"]], " ", SubscriptBox["a_", "4"]]], "+", RowBox[List[SubscriptBox["a_", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Log", "[", "s_", "]"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["a_", "4"]]]]], ")"]]]], "+", RowBox[List[SubscriptBox["a_", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Log", "[", "s_", "]"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["a_", "3"], "+", SubscriptBox["a_", "4"]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", "a_", " ", SuperscriptBox["r_", "z_"], " ", SuperscriptBox[RowBox[List["Log", "[", "s_", "]"]], "2"], " ", SubscriptBox["a_", "4"]]], "-", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"], " ", RowBox[List["Log", "[", "s_", "]"]], " ", SubscriptBox["a_", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", RowBox[List["Log", "[", "s_", "]"]]]], "-", RowBox[List["2", " ", RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["a_", "4"]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], "+", RowBox[List["Log", "[", "s_", "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], "+", RowBox[List["3", " ", RowBox[List["Log", "[", "s_", "]"]]]]]], ")"]], " ", SubscriptBox["b_", "3"]]], "+", RowBox[List[SubscriptBox["b_", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], "+", RowBox[List["Log", "[", "s_", "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], "+", RowBox[List["3", " ", RowBox[List["Log", "[", "s_", "]"]]]]]], ")"]]]], "-", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], "+", RowBox[List["2", " ", RowBox[List["Log", "[", "s_", "]"]]]]]], ")"]], " ", SubscriptBox["b_", "3"]]]]], ")"]]]], "+", RowBox[List[SubscriptBox["b_", "1"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], "+", RowBox[List["Log", "[", "s_", "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], "+", RowBox[List["3", " ", RowBox[List["Log", "[", "s_", "]"]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], "+", RowBox[List["2", " ", RowBox[List["Log", "[", "s_", "]"]]]]]], ")"]]]], " ", SubscriptBox["b_", "3"]]], "+", RowBox[List[SubscriptBox["b_", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", "r_", "]"]]]], "-", RowBox[List["2", " ", RowBox[List["Log", "[", "s_", "]"]]]], "+", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["b_", "3"]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"]]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["a_", " ", SuperscriptBox["r_", "z_"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "s_", "]"]], "-", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["a_", "1"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "s_", "]"]], "-", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["a_", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "s_", "]"]], "-", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["a_", "3"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "s_", "]"]], "-", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["a_", "4"]]]]], ")"]]]], "-", RowBox[List[RowBox[List["Log", "[", "s_", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], "+", RowBox[List["Log", "[", "s_", "]"]], "-", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["b_", "1"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], "+", RowBox[List["Log", "[", "s_", "]"]], "-", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["b_", "2"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], "+", RowBox[List["Log", "[", "s_", "]"]], "-", RowBox[List[RowBox[List["Log", "[", "r_", "]"]], " ", SubscriptBox["b_", "3"]]]]], ")"]]]]]], ")"]], " ", RowBox[List["w", "[", "z_", "]"]]]], RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"]]]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[SubscriptBox["c", "1"], " ", SuperscriptBox["s", "z"], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", SubscriptBox["a", "2"], ",", SubscriptBox["a", "3"], ",", SubscriptBox["a", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"], ",", SubscriptBox["b", "3"]]], "}"]], ",", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "2"], " ", SuperscriptBox["s", "z"], " ", RowBox[List["(", RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "3"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "4"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", SubscriptBox["b", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["b", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "3"]]]]], "}"]]]], "}"]], ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]], "+", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "3"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "4"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", SubscriptBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "3"]]]]], "}"]]]], "}"]], ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]], "+", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "3"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "4"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", SubscriptBox["b", "3"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "2"]]]]], "}"]]]], "}"]], ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]]]], ")"]]]], "+", RowBox[List[SubscriptBox["c", "3"], " ", SuperscriptBox["s", "z"], " ", RowBox[List["(", RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "3"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "4"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "-", SubscriptBox["b", "3"]]], "}"]]]], "}"]], ",", RowBox[List[RowBox[List["-", "a"]], " ", SuperscriptBox["r", "z"]]]]], "]"]], "+", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "3"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "4"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "3"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "-", SubscriptBox["b", "2"]]], "}"]]]], "}"]], ",", RowBox[List[RowBox[List["-", "a"]], " ", SuperscriptBox["r", "z"]]]]], "]"]], "+", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "3"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "4"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", SubscriptBox["b", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "3"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "-", SubscriptBox["b", "1"]]], "}"]]]], "}"]], ",", RowBox[List[RowBox[List["-", "a"]], " ", SuperscriptBox["r", "z"]]]]], "]"]]]], ")"]]]], "+", RowBox[List[SubscriptBox["c", "4"], " ", SuperscriptBox["s", "z"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "3"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "4"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["b", "3"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["a", " ", SuperscriptBox["r", "z"]]]]], "]"]]]]]]]]]]]]]]










Date Added to functions.wolfram.com (modification date)





2007-05-02





© 1998- Wolfram Research, Inc.