Generalized hypergeometric function 2F3: Differential equations (formula 07.26.13.0003)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]

Differential equations

Ordinary linear differential equations and wronskians

For the direct function itself

http://functions.wolfram.com/07.26.13.0003.01

Input Form

Wronskian[HypergeometricPFQRegularized[{Subscript[a, 1], Subscript[a, 2]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2]}, {}}, {{0, 1 - Subscript[b, 1]}, {1 - Subscript[b, 2], 1 - Subscript[b, 3]}}, z] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2]}, {}}, {{0, 1 - Subscript[b, 2]}, {1 - Subscript[b, 1], 1 - Subscript[b, 3]}}, z] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2]}, {}}, {{0, 1 - Subscript[b, 3]}, {1 - Subscript[b, 1], 1 - Subscript[b, 2]}}, z], MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2]}, {}}, {{0, 1 - Subscript[b, 1], 1 - Subscript[b, 2]}, {1 - Subscript[b, 3]}}, -z] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2]}, {}}, {{0, 1 - Subscript[b, 1], 1 - Subscript[b, 3]}, {1 - Subscript[b, 2]}}, -z] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2]}, {}}, {{0, 1 - Subscript[b, 2], 1 - Subscript[b, 3]}, {1 - Subscript[b, 1]}}, -z], MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2]}, {}}, {{0, 1 - Subscript[b, 1], 1 - Subscript[b, 2], 1 - Subscript[b, 3]}, {}}, z], z] == (-z)^(-Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3]) z^(-3 - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3]) ((-(-z)^(Subscript[b, 2] + Subscript[b, 3])) z^Subscript[b, 1] (Csc[Pi (Subscript[b, 1] - Subscript[b, 3])] Sin[Pi (Subscript[b, 1] - Subscript[b, 2])] + Csc[Pi (Subscript[b, 1] - Subscript[b, 2])] Sin[Pi (Subscript[b, 1] - Subscript[b, 3])]) + (-z)^(Subscript[b, 1] + Subscript[b, 3]) z^Subscript[b, 2] (Csc[Pi (Subscript[b, 1] - Subscript[b, 2])]^2 + Csc[Pi (Subscript[b, 2] - Subscript[b, 3])]^2) Sin[Pi (Subscript[b, 1] - Subscript[b, 2])] Sin[Pi (Subscript[b, 2] - Subscript[b, 3])] - (-z)^(Subscript[b, 1] + Subscript[b, 2]) z^Subscript[b, 3] (Csc[Pi (Subscript[b, 1] - Subscript[b, 3])]^2 + Csc[Pi (Subscript[b, 2] - Subscript[b, 3])]^2) Sin[Pi (Subscript[b, 1] - Subscript[b, 3])] Sin[Pi (Subscript[b, 2] - Subscript[b, 3])] - 2 ((-z)^(Subscript[b, 2] + Subscript[b, 3]) z^Subscript[b, 1] + (-z)^(Subscript[b, 1] + Subscript[b, 3]) z^Subscript[b, 2] + (-z)^(Subscript[b, 1] + Subscript[b, 2]) z^Subscript[b, 3])) Gamma[1 + Subscript[a, 1] - Subscript[b, 1]] Gamma[1 + Subscript[a, 2] - Subscript[b, 1]] Gamma[1 + Subscript[a, 1] - Subscript[b, 2]] Gamma[1 + Subscript[a, 2] - Subscript[b, 2]] Gamma[1 + Subscript[a, 1] - Subscript[b, 3]] Gamma[1 + Subscript[a, 2] - Subscript[b, 3]]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", SubscriptBox["a", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"], ",", SubscriptBox["b", "3"]]], "}"]], ",", "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["{", "}"]]]], "}"]], ",", 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"]]]]], "}"]]]], "}"]], ",", "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["{", "}"]]]], "}"]], ",", 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"]]]]], "}"]]]], "}"]], ",", "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["{", "}"]]]], "}"]], ",", 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"]]]]], "}"]]]], "}"]], ",", "z"]], "]"]]]], ",", 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["{", "}"]]]], "}"]], ",", 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["-", "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["{", "}"]]]], "}"]], ",", 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["-", "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["{", "}"]]]], "}"]], ",", 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["-", "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["{", "}"]]]], "}"]], ",", 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["{", "}"]]]], "}"]], ",", "z"]], "]"]], ",", " ", "z"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List[RowBox[List["-", SubscriptBox["b", "1"]]], "-", SubscriptBox["b", "2"], "-", SubscriptBox["b", "3"]]]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "3"]], "-", SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"], "-", SubscriptBox["b", "3"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List[SubscriptBox["b", "2"], "+", SubscriptBox["b", "3"]]]]]], " ", SuperscriptBox["z", SubscriptBox["b", "1"]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["b", "1"], "-", SubscriptBox["b", "3"]]], ")"]]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"]]], ")"]]]], "]"]]]], "+", RowBox[List[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"]]], ")"]]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["b", "1"], "-", SubscriptBox["b", "3"]]], ")"]]]], "]"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List[SubscriptBox["b", "1"], "+", SubscriptBox["b", "3"]]]], " ", SuperscriptBox["z", SubscriptBox["b", "2"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"]]], ")"]]]], "]"]], "2"], "+", SuperscriptBox[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["b", "2"], "-", SubscriptBox["b", "3"]]], ")"]]]], "]"]], "2"]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"]]], ")"]]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["b", "2"], "-", SubscriptBox["b", "3"]]], ")"]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List[SubscriptBox["b", "1"], "+", SubscriptBox["b", "2"]]]], " ", SuperscriptBox["z", SubscriptBox["b", "3"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["b", "1"], "-", SubscriptBox["b", "3"]]], ")"]]]], "]"]], "2"], "+", SuperscriptBox[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["b", "2"], "-", SubscriptBox["b", "3"]]], ")"]]]], "]"]], "2"]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["b", "1"], "-", SubscriptBox["b", "3"]]], ")"]]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["b", "2"], "-", SubscriptBox["b", "3"]]], ")"]]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List[SubscriptBox["b", "2"], "+", SubscriptBox["b", "3"]]]], " ", SuperscriptBox["z", SubscriptBox["b", "1"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List[SubscriptBox["b", "1"], "+", SubscriptBox["b", "3"]]]], " ", SuperscriptBox["z", SubscriptBox["b", "2"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List[SubscriptBox["b", "1"], "+", SubscriptBox["b", "2"]]]], " ", SuperscriptBox["z", SubscriptBox["b", "3"]]]]]], ")"]]]]]], ")"]], RowBox[List["Gamma", "[", RowBox[List["1", "+", SubscriptBox["a", "1"], "-", SubscriptBox["b", "1"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", SubscriptBox["a", "2"], "-", SubscriptBox["b", "1"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", SubscriptBox["a", "1"], "-", SubscriptBox["b", "2"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", SubscriptBox["a", "2"], "-", SubscriptBox["b", "2"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", SubscriptBox["a", "1"], "-", SubscriptBox["b", "3"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", SubscriptBox["a", "2"], "-", SubscriptBox["b", "3"]]], "]"]]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> W </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mrow> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mn> 3 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> a </mi> <mn> 2 </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> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox[OverscriptBox["F", "~"], "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "2"], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "3"], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] </annotation> </semantics> <mo> + </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </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> </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["G", MeijerG], RowBox[List["2", ",", "4"]], RowBox[List["2", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "2"]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "2"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "3"]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> <mo> + </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </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> </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["G", MeijerG], RowBox[List["2", ",", "4"]], RowBox[List["2", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "2"]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "2"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "3"]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> <mo> + </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </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> </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["G", MeijerG], RowBox[List["2", ",", "4"]], RowBox[List["2", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "2"]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "3"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "2"]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> </mrow> <mo> , </mo> <mrow> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 3 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ❘ </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> </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["G", MeijerG], RowBox[List["2", ",", "4"]], RowBox[List["3", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List["-", "z"]], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "2"]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "2"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "3"]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> <mo> + </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 3 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ❘ </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> </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["G", MeijerG], RowBox[List["2", ",", "4"]], RowBox[List["3", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List["-", "z"]], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "2"]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "3"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "2"]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> <mo> + </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 3 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ❘ </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> </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["G", MeijerG], RowBox[List["2", ",", "4"]], RowBox[List["3", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List["-", "z"]], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "2"]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "2"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "3"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "1"]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> </mrow> <mo> , </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 4 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </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> </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["G", MeijerG], RowBox[List["2", ",", "4"]], RowBox[List["4", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "2"]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "2"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "3"]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mrow> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> - </mo> <mn> 3 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> </msup> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> csc </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mi> csc </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> csc </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msup> <mi> csc </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <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> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <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> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </msup> </mrow> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> csc </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msup> <mi> csc </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <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> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <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> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <ci> z </ci> </apply> <apply> <plus /> <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> </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> <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> </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> <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> </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> <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> </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> <ci> z </ci> </apply> </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> </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 /> <cn type='integer'> -1 </cn> <ci> z </ci> </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> </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 /> <cn type='integer'> -1 </cn> <ci> z </ci> </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> </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 /> <cn type='integer'> -1 </cn> <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> </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> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -3 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <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> </apply> <apply> <plus /> <apply> <times /> <apply> <csc /> <apply> <times /> <pi /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <pi /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <csc /> <apply> <times /> <pi /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <pi /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </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'> 3 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <power /> <apply> <csc /> <apply> <times /> <pi /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <csc /> <apply> <times /> <pi /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <sin /> <apply> <times /> <pi /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <pi /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </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> </apply> <apply> <plus /> <apply> <power /> <apply> <csc /> <apply> <times /> <pi /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <csc /> <apply> <times /> <pi /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <sin /> <apply> <times /> <pi /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <pi /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <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> <apply> <power /> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </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'> 3 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </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> </apply> <apply> <power /> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", SubscriptBox["a_", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", SubscriptBox["b_", "2"], ",", SubscriptBox["b_", "3"]]], "}"]], ",", "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["{", "}"]]]], "}"]], ",", 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"]]]]], "}"]]]], "}"]], ",", "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["{", "}"]]]], "}"]], ",", 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"]]]]], "}"]]]], "}"]], ",", "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["{", "}"]]]], "}"]], ",", 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"]]]]], "}"]]]], "}"]], ",", "z_"]], "]"]]]], ",", 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["{", "}"]]]], "}"]], ",", 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["-", "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["{", "}"]]]], "}"]], ",", 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["-", "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["{", "}"]]]], "}"]], ",", 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["-", "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["{", "}"]]]], "}"]], ",", 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["{", "}"]]]], "}"]], ",", "z_"]], "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List[RowBox[List["-", SubscriptBox["bb", "1"]]], "-", SubscriptBox["bb", "2"], "-", SubscriptBox["bb", "3"]]]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "3"]], "-", SubscriptBox["bb", "1"], "-", SubscriptBox["bb", "2"], "-", SubscriptBox["bb", "3"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List[SubscriptBox["bb", "2"], "+", SubscriptBox["bb", "3"]]]]]], " ", SuperscriptBox["z", SubscriptBox["bb", "1"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["bb", "1"], "-", SubscriptBox["bb", "3"]]], ")"]]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["bb", "1"], "-", SubscriptBox["bb", "2"]]], ")"]]]], "]"]]]], "+", RowBox[List[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["bb", "1"], "-", SubscriptBox["bb", "2"]]], ")"]]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["bb", "1"], "-", SubscriptBox["bb", "3"]]], ")"]]]], "]"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List[SubscriptBox["bb", "1"], "+", SubscriptBox["bb", "3"]]]], " ", SuperscriptBox["z", SubscriptBox["bb", "2"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["bb", "1"], "-", SubscriptBox["bb", "2"]]], ")"]]]], "]"]], "2"], "+", SuperscriptBox[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["bb", "2"], "-", SubscriptBox["bb", "3"]]], ")"]]]], "]"]], "2"]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["bb", "1"], "-", SubscriptBox["bb", "2"]]], ")"]]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["bb", "2"], "-", SubscriptBox["bb", "3"]]], ")"]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List[SubscriptBox["bb", "1"], "+", SubscriptBox["bb", "2"]]]], " ", SuperscriptBox["z", SubscriptBox["bb", "3"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["bb", "1"], "-", SubscriptBox["bb", "3"]]], ")"]]]], "]"]], "2"], "+", SuperscriptBox[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["bb", "2"], "-", SubscriptBox["bb", "3"]]], ")"]]]], "]"]], "2"]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["bb", "1"], "-", SubscriptBox["bb", "3"]]], ")"]]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["bb", "2"], "-", SubscriptBox["bb", "3"]]], ")"]]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List[SubscriptBox["bb", "2"], "+", SubscriptBox["bb", "3"]]]], " ", SuperscriptBox["z", SubscriptBox["bb", "1"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List[SubscriptBox["bb", "1"], "+", SubscriptBox["bb", "3"]]]], " ", SuperscriptBox["z", SubscriptBox["bb", "2"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List[SubscriptBox["bb", "1"], "+", SubscriptBox["bb", "2"]]]], " ", SuperscriptBox["z", SubscriptBox["bb", "3"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", SubscriptBox["aa", "1"], "-", SubscriptBox["bb", "1"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", SubscriptBox["aa", "2"], "-", SubscriptBox["bb", "1"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", SubscriptBox["aa", "1"], "-", SubscriptBox["bb", "2"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", SubscriptBox["aa", "2"], "-", SubscriptBox["bb", "2"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", SubscriptBox["aa", "1"], "-", SubscriptBox["bb", "3"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", SubscriptBox["aa", "2"], "-", SubscriptBox["bb", "3"]]], "]"]]]]]]]]

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

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]