Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

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
MeijerG




Mathematica Notation

Traditional Notation









Hypergeometric Functions > MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z] > Specific values > Specialized values > Cases with arbitrary {m,n,p,q} > Case {m,n,p,q}={1,p,p,q}





http://functions.wolfram.com/07.34.03.0009.01









  


  








Input Form





MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {}}, {{0}, {Subscript[a, 1] - Subscript[m, 1], \[Ellipsis], Subscript[a, n] - Subscript[m, n], Subscript[b, n + 1], \[Ellipsis], Subscript[b, q]}}, z] == (Product[Gamma[1 - Subscript[a, j]], {j, n + 1, p}]/ (Product[(Subscript[m, j] - 1)!, {j, 1, n}] Product[Gamma[1 - Subscript[b, j]], {j, n + 1, q}])) Sum[\[Ellipsis] Sum[(1/(1 - Subscript[a, k] + Subscript[j, k])) Product[(Pochhammer[1 - Subscript[m, l], Subscript[j, l]]/ Subscript[j, l]!) Product[If[i == k, 1, 1/(Subscript[a, k] + Subscript[j, i] - Subscript[a, i] - Subscript[j, k])] HypergeometricPFQ[{1 - Subscript[a, k] + Subscript[j, k], 1 - Subscript[a, n + 1], \[Ellipsis], 1 - Subscript[a, p]}, {2 - Subscript[a, k] + Subscript[j, k], 1 - Subscript[b, n + 1], \[Ellipsis], 1 - Subscript[b, q]}, -z], {i, 1, n}], {l, 1, n}], {Subscript[j, n], 0, Subscript[m, n] - 1}], {k, 1, n}, {Subscript[j, 1], 0, Subscript[m, 1] - 1}] /; Element[Subscript[m, n], Integers] && Subscript[m, n] > 0 && n <= q








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["a", "1"], "-", SubscriptBox["m", "1"]]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", "n"], "-", SubscriptBox["m", "n"]]], ",", SubscriptBox["b", RowBox[List["n", "+", "1"]]], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", RowBox[List["n", "+", "1"]]]], "p"], RowBox[List["Gamma", "[", RowBox[List["1", "-", SubscriptBox["a", "j"]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "n"], RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["m", "j"], "-", "1"]], ")"]], "!"]]]], ")"]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", RowBox[List["n", "+", "1"]]]], "q"], RowBox[List["Gamma", "[", RowBox[List["1", "-", SubscriptBox["b", "j"]]], "]"]]]]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["j", "1"], "=", "0"]], RowBox[List[SubscriptBox["m", "1"], "-", "1"]]], RowBox[List["\[Ellipsis]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["j", "n"], "=", "0"]], RowBox[List[SubscriptBox["m", "n"], "-", "1"]]], RowBox[List[FractionBox["1", RowBox[List["1", "-", SubscriptBox["a", "k"], "+", SubscriptBox["j", "k"]]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["l", "=", "1"]], "n"], RowBox[List[FractionBox[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", SubscriptBox["m", "l"]]], ",", SubscriptBox["j", "l"]]], "]"]], RowBox[List[SubscriptBox["j", "l"], "!"]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["i", "=", "1"]], "n"], RowBox[List[RowBox[List["If", "[", RowBox[List[RowBox[List["i", "\[Equal]", "k"]], ",", "1", ",", FractionBox["1", RowBox[List[SubscriptBox["a", "k"], "+", SubscriptBox["j", "i"], "-", SubscriptBox["a", "i"], "-", SubscriptBox["j", "k"]]]]]], "]"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "k"], "+", SubscriptBox["j", "k"]]], ",", RowBox[List["1", "-", SubscriptBox["a", RowBox[List["n", "+", "1"]]]]], ",", "\[Ellipsis]", ",", RowBox[List["1", "-", SubscriptBox["a", "p"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "-", SubscriptBox["a", "k"], "+", SubscriptBox["j", "k"]]], ",", RowBox[List["1", "-", SubscriptBox["b", RowBox[List["n", "+", "1"]]]]], ",", "\[Ellipsis]", ",", RowBox[List["1", "-", SubscriptBox["b", "q"]]]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]]]]]]]]]]]]]]]]]]]]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["m", "n"], "\[Element]", "Integers"]], "\[And]", RowBox[List[SubscriptBox["m", "n"], ">", "0"]], "\[And]", RowBox[List["n", "\[LessEqual]", "q"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mi> p </mi> <mo> , </mo> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> p </mi> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> a </mi> <mi> p </mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <msub> <mi> a </mi> <mi> n </mi> </msub> <mo> - </mo> <msub> <mi> m </mi> <mi> n </mi> </msub> </mrow> <mo> , </mo> <msub> <mi> b </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> b </mi> <mi> q </mi> </msub> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;p&quot;, &quot;,&quot;, RowBox[List[&quot;q&quot;, &quot;+&quot;, &quot;1&quot;]]]], RowBox[List[&quot;1&quot;, &quot;,&quot;, &quot;p&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[&quot;z&quot;, MeijerG, Rule[Editable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[SubscriptBox[&quot;a&quot;, &quot;1&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;a&quot;, &quot;p&quot;], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;a&quot;, &quot;1&quot;], &quot;-&quot;, SubscriptBox[&quot;m&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;a&quot;, &quot;n&quot;], &quot;-&quot;, SubscriptBox[&quot;m&quot;, &quot;n&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;b&quot;, RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;b&quot;, &quot;q&quot;], MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, True]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mfrac> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mi> p </mi> </munderover> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> m </mi> <mi> j </mi> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mi> q </mi> </munderover> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <msub> <mi> m </mi> <mn> 1 </mn> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <mo> &#8230; </mo> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> j </mi> <mi> n </mi> </msub> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <msub> <mi> m </mi> <mi> n </mi> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <mfrac> <mn> 1 </mn> <mrow> <msub> <mi> j </mi> <mi> k </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> l </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mfrac> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> m </mi> <mi> l </mi> </msub> </mrow> <mo> ) </mo> </mrow> <msub> <mi> j </mi> <mi> l </mi> </msub> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;m&quot;, &quot;l&quot;]]], &quot;)&quot;]], SubscriptBox[&quot;j&quot;, &quot;l&quot;]], Pochhammer] </annotation> </semantics> <mrow> <msub> <mi> j </mi> <mi> l </mi> </msub> <mo> ! </mo> </mrow> </mfrac> <mo> &#8290; </mo> <munderover> <mrow> <mtext> </mtext> <mo> &#8719; </mo> </mrow> <munder> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <mi> j </mi> <mo> &#8800; </mo> <mi> k </mi> </mrow> </munder> <mi> n </mi> </munderover> <mo> &#8290; </mo> <mfrac> <mn> 1 </mn> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> i </mi> </msub> <mo> + </mo> <msub> <mi> j </mi> <mi> i </mi> </msub> <mo> - </mo> <msub> <mi> j </mi> <mi> k </mi> </msub> </mrow> </mfrac> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mrow> <mi> p </mi> <mo> - </mo> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <msub> <mi> F </mi> <mrow> <mi> q </mi> <mo> - </mo> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <msub> <mi> j </mi> <mi> k </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mi> p </mi> </msub> </mrow> </mrow> <mo> ; </mo> <mrow> <mrow> <msub> <mi> j </mi> <mi> k </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mi> q </mi> </msub> </mrow> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[RowBox[List[&quot;p&quot;, &quot;-&quot;, &quot;n&quot;, &quot;+&quot;, &quot;1&quot;]], TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[RowBox[List[&quot;q&quot;, &quot;-&quot;, &quot;n&quot;, &quot;+&quot;, &quot;1&quot;]], TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[SubscriptBox[&quot;j&quot;, &quot;k&quot;], &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;k&quot;], &quot;+&quot;, &quot;1&quot;]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;1&quot;]]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;p&quot;]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[RowBox[List[SubscriptBox[&quot;j&quot;, &quot;k&quot;], &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;k&quot;], &quot;+&quot;, &quot;2&quot;]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;1&quot;]]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;q&quot;]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;;&quot;, TagBox[RowBox[List[&quot;-&quot;, &quot;z&quot;]], HypergeometricPFQ, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] </annotation> </semantics> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> m </mi> <mi> n </mi> </msub> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8804; </mo> <mi> q </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mi> p </mi> <mo> , </mo> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> p </mi> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> a </mi> <mi> p </mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <msub> <mi> a </mi> <mi> n </mi> </msub> <mo> - </mo> <msub> <mi> m </mi> <mi> n </mi> </msub> </mrow> <mo> , </mo> <msub> <mi> b </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> b </mi> <mi> q </mi> </msub> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;p&quot;, &quot;,&quot;, RowBox[List[&quot;q&quot;, &quot;+&quot;, &quot;1&quot;]]]], RowBox[List[&quot;1&quot;, &quot;,&quot;, &quot;p&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[&quot;z&quot;, MeijerG, Rule[Editable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[SubscriptBox[&quot;a&quot;, &quot;1&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;a&quot;, &quot;p&quot;], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;a&quot;, &quot;1&quot;], &quot;-&quot;, SubscriptBox[&quot;m&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;a&quot;, &quot;n&quot;], &quot;-&quot;, SubscriptBox[&quot;m&quot;, &quot;n&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;b&quot;, RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;b&quot;, &quot;q&quot;], MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, True]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mfrac> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mi> p </mi> </munderover> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> m </mi> <mi> j </mi> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mi> q </mi> </munderover> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <msub> <mi> m </mi> <mn> 1 </mn> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <mo> &#8230; </mo> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> j </mi> <mi> n </mi> </msub> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <msub> <mi> m </mi> <mi> n </mi> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <mfrac> <mn> 1 </mn> <mrow> <msub> <mi> j </mi> <mi> k </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> l </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mfrac> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> m </mi> <mi> l </mi> </msub> </mrow> <mo> ) </mo> </mrow> <msub> <mi> j </mi> <mi> l </mi> </msub> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;m&quot;, &quot;l&quot;]]], &quot;)&quot;]], SubscriptBox[&quot;j&quot;, &quot;l&quot;]], Pochhammer] </annotation> </semantics> <mrow> <msub> <mi> j </mi> <mi> l </mi> </msub> <mo> ! </mo> </mrow> </mfrac> <mo> &#8290; </mo> <munderover> <mrow> <mtext> </mtext> <mo> &#8719; </mo> </mrow> <munder> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <mi> j </mi> <mo> &#8800; </mo> <mi> k </mi> </mrow> </munder> <mi> n </mi> </munderover> <mo> &#8290; </mo> <mfrac> <mn> 1 </mn> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> i </mi> </msub> <mo> + </mo> <msub> <mi> j </mi> <mi> i </mi> </msub> <mo> - </mo> <msub> <mi> j </mi> <mi> k </mi> </msub> </mrow> </mfrac> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mrow> <mi> p </mi> <mo> - </mo> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <msub> <mi> F </mi> <mrow> <mi> q </mi> <mo> - </mo> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <msub> <mi> j </mi> <mi> k </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mi> p </mi> </msub> </mrow> </mrow> <mo> ; </mo> <mrow> <mrow> <msub> <mi> j </mi> <mi> k </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mi> q </mi> </msub> </mrow> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[RowBox[List[&quot;p&quot;, &quot;-&quot;, &quot;n&quot;, &quot;+&quot;, &quot;1&quot;]], TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[RowBox[List[&quot;q&quot;, &quot;-&quot;, &quot;n&quot;, &quot;+&quot;, &quot;1&quot;]], TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[SubscriptBox[&quot;j&quot;, &quot;k&quot;], &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;k&quot;], &quot;+&quot;, &quot;1&quot;]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;1&quot;]]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;p&quot;]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[RowBox[List[SubscriptBox[&quot;j&quot;, &quot;k&quot;], &quot;-&quot;, SubscriptBox[&quot;a&quot;, &quot;k&quot;], &quot;+&quot;, &quot;2&quot;]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;1&quot;]]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;b&quot;, &quot;q&quot;]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], &quot;;&quot;, TagBox[RowBox[List[&quot;-&quot;, &quot;z&quot;]], HypergeometricPFQ, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] </annotation> </semantics> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> m </mi> <mi> n </mi> </msub> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8804; </mo> <mi> q </mi> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










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





2001-10-29