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Hypergeometric Functions
MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z]
Transformations
Products, sums, and powers of the direct function
Products of the direct function
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http://functions.wolfram.com/07.34.16.0003.01
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MeijerG[{{Subscript[a, 11], \[Ellipsis], Subscript[a, 1 Subscript[n, 1]]},
{Subscript[a, 1 Subscript[n, 1] + 1], \[Ellipsis],
Subscript[a, 1 Subscript[p, 1]]}},
{{Subscript[b, 11], \[Ellipsis], Subscript[b, 1 Subscript[m, 1]]},
{Subscript[b, 1 Subscript[m, 1] + 1], \[Ellipsis],
Subscript[b, 1 Subscript[q, 1]]}}, z]
MeijerG[{{Subscript[a, 21], \[Ellipsis], Subscript[a, 2 Subscript[n, 2]]},
{Subscript[a, 2 Subscript[n, 2] + 1], \[Ellipsis],
Subscript[a, 2 Subscript[p, 2]]}},
{{Subscript[b, 21], \[Ellipsis], Subscript[b, 2 Subscript[m, 2]]},
{Subscript[b, 2 Subscript[m, 2] + 1], \[Ellipsis],
Subscript[b, 2 Subscript[q, 2]]}}, w] == MeijerG[{{{}, {}}, {{}, {}}},
{{{Subscript[a, 11], \[Ellipsis], Subscript[a, 1 Subscript[n, 1]]},
{Subscript[a, 1 Subscript[n, 1] + 1], \[Ellipsis],
Subscript[a, 1 Subscript[p, 1]]}},
{{Subscript[b, 11], \[Ellipsis], Subscript[b, 1 Subscript[m, 1]]},
{Subscript[b, 1 Subscript[m, 1] + 1], \[Ellipsis],
Subscript[b, 1 Subscript[q, 1]]}}},
{{{Subscript[a, 21], \[Ellipsis], Subscript[a, 2 Subscript[n, 2]]},
{Subscript[a, 2 Subscript[n, 2] + 1], \[Ellipsis],
Subscript[a, 2 Subscript[p, 2]]}},
{{Subscript[b, 21], \[Ellipsis], Subscript[b, 2 Subscript[m, 2]]},
{Subscript[b, 2 Subscript[m, 2] + 1], \[Ellipsis],
Subscript[b, 2 Subscript[q, 2]]}}}, z, w]
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<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> <msub> <mi> p </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> q </mi> <mn> 1 </mn> </msub> </mrow> <mrow> <msub> <mi> m </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> n </mi> <mn> 1 </mn> </msub> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mtable> <mtr> <mtd> <mrow> <msub> <mi> a </mi> <mn> 11 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> a </mi> <mrow> <mn> 1 </mn> <mo> ⁢ </mo> <msub> <mi> n </mi> <mn> 1 </mn> </msub> </mrow> </msub> <mo> , </mo> <msub> <mi> a </mi> <mrow> <mrow> <mn> 1 </mn> <mo> ⁢ </mo> <msub> <mi> n </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> a </mi> <mrow> <mn> 1 </mn> <mo> ⁢ </mo> <msub> <mi> p </mi> <mn> 1 </mn> </msub> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> b </mi> <mn> 11 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> b </mi> <mrow> <mn> 1 </mn> <mo> ⁢ </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mrow> </msub> <mo> , </mo> <msub> <mi> b </mi> <mrow> <mrow> <mn> 1 </mn> <mo> ⁢ </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> b </mi> <mrow> <mn> 1 </mn> <mo> ⁢ </mo> <msub> <mi> q </mi> <mn> 1 </mn> </msub> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List[SubscriptBox["p", "1"], ",", SubscriptBox["q", "1"]]], RowBox[List[SubscriptBox["m", "1"], ",", SubscriptBox["n", "1"]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", 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</mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> b </mi> <mn> 21 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> b </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mrow> </msub> <mo> , </mo> <msub> <mi> b </mi> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> b </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> q </mi> <mn> 2 </mn> </msub> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List[SubscriptBox["p", "2"], ",", SubscriptBox["q", "2"]]], RowBox[List[SubscriptBox["m", "2"], ",", SubscriptBox["n", "2"]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["w", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", 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</mtd> </mtr> </mtable> <mo> ⁢ </mo> <mtable> <mtr> <mtd> <mrow> <mo fontfamily='Times'> … </mo> <mo> , </mo> </mrow> </mtd> <mtd> <msub> <mi> a </mi> <mrow> <mn> 1 </mn> <mo> ⁢ </mo> <msub> <mi> p </mi> <mn> 1 </mn> </msub> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo fontfamily='Times'> … </mo> <mo> , </mo> </mrow> </mtd> <mtd> <msub> <mi> b </mi> <mrow> <mn> 1 </mn> <mo> ⁢ </mo> <msub> <mi> q </mi> <mn> 1 </mn> </msub> </mrow> </msub> </mtd> </mtr> </mtable> </mrow> <mo> ❘ </mo> <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi> a </mi> <mn> 21 </mn> </msub> <mo> , </mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> b </mi> <mn> 21 </mn> </msub> <mo> , </mo> </mrow> </mtd> </mtr> </mtable> <mo> ⁢ </mo> <mtable> <mtr> <mtd> <mrow> <mo fontfamily='Times'> … </mo> <mo> , </mo> </mrow> </mtd> <mtd> <msub> <mi> a </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> p </mi> <mn> 2 </mn> </msub> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo fontfamily='Times'> … </mo> <mo> 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</mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> a </mi> <mrow> <mn> 1 </mn> <mo> ⁢ </mo> <msub> <mi> p </mi> <mn> 1 </mn> </msub> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> b </mi> <mn> 11 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> b </mi> <mrow> <mn> 1 </mn> <mo> ⁢ </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mrow> </msub> <mo> , </mo> <msub> <mi> b </mi> <mrow> <mrow> <mn> 1 </mn> <mo> ⁢ </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> b </mi> <mrow> <mn> 1 </mn> <mo> ⁢ </mo> <msub> <mi> q </mi> <mn> 1 </mn> </msub> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List[SubscriptBox["p", "1"], ",", SubscriptBox["q", "1"]]], 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</mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> a </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> p </mi> <mn> 2 </mn> </msub> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> b </mi> <mn> 21 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> b </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mrow> </msub> <mo> , </mo> <msub> <mi> b </mi> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> b </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> q </mi> <mn> 2 </mn> </msub> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List[SubscriptBox["p", "2"], ",", SubscriptBox["q", 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</mo> <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi> a </mi> <mn> 11 </mn> </msub> <mo> , </mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> b </mi> <mn> 11 </mn> </msub> <mo> , </mo> </mrow> </mtd> </mtr> </mtable> <mo> ⁢ </mo> <mtable> <mtr> <mtd> <mrow> <mo fontfamily='Times'> … </mo> <mo> , </mo> </mrow> </mtd> <mtd> <msub> <mi> a </mi> <mrow> <mn> 1 </mn> <mo> ⁢ </mo> <msub> <mi> p </mi> <mn> 1 </mn> </msub> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo fontfamily='Times'> … </mo> <mo> , </mo> </mrow> </mtd> <mtd> <msub> <mi> b </mi> <mrow> <mn> 1 </mn> <mo> ⁢ </mo> <msub> <mi> q </mi> <mn> 1 </mn> </msub> </mrow> </msub> </mtd> </mtr> </mtable> </mrow> <mo> ❘ </mo> <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi> a </mi> <mn> 21 </mn> </msub> <mo> , </mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> b </mi> <mn> 21 </mn> </msub> <mo> , </mo> </mrow> </mtd> </mtr> </mtable> <mo> ⁢ </mo> <mtable> <mtr> <mtd> <mrow> <mo fontfamily='Times'> … </mo> <mo> , </mo> </mrow> </mtd> <mtd> <msub> <mi> a </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> p </mi> <mn> 2 </mn> </msub> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo fontfamily='Times'> … </mo> <mo> , </mo> </mrow> </mtd> <mtd> <msub> <mi> b </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> q </mi> <mn> 2 </mn> </msub> </mrow> </msub> </mtd> </mtr> </mtable> </mrow> <mo> ❘ </mo> <mi> z </mi> </mrow> <mo> , </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z,r] | |
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