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Hypergeometric Functions
MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z]
Identities
Functional identities
General cases
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http://functions.wolfram.com/07.34.17.0011.01
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MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, n]},
{Subscript[a, n + 1], \[Ellipsis], Subscript[a, p]}},
{{Subscript[b, 1], \[Ellipsis], Subscript[b, m]},
{Subscript[b, m + 1], \[Ellipsis], Subscript[b, q]}}, z] ==
MeijerG[{{Subscript[a, 1] + \[Alpha], \[Ellipsis],
Subscript[a, n] + \[Alpha]}, {Subscript[a, n + 1] + \[Alpha],
\[Ellipsis], Subscript[a, p] + \[Alpha]}},
{{Subscript[b, 1] + \[Alpha], \[Ellipsis], Subscript[b, m] + \[Alpha]},
{Subscript[b, m + 1] + \[Alpha], \[Ellipsis],
Subscript[b, q] + \[Alpha]}}, z]/z^\[Alpha]
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</mn> </mrow> </msub> </mrow> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mrow> <mi> α </mi> <mo> + </mo> <msub> <mi> a </mi> <mi> p </mi> </msub> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mi> α </mi> <mo> + </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mrow> <mi> α </mi> <mo> + </mo> <msub> <mi> b </mi> <mi> m </mi> </msub> </mrow> <mo> , </mo> <mrow> <mi> α </mi> <mo> + </mo> <msub> <mi> b </mi> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mrow> <mi> α </mi> <mo> + </mo> <msub> <mi> b </mi> <mi> q </mi> </msub> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["p", ",", "q"]], RowBox[List["m", ",", "n"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", 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b </mi> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> … </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["G", MeijerG], RowBox[List["p", ",", "q"]], RowBox[List["m", ",", "n"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[SubscriptBox["a", "1"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "n"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", RowBox[List["n", "+", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "p"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[SubscriptBox["b", "1"], MeijerG, 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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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