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Hypergeometric Functions
MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z]
Specific values
Specialized values
Cases with m==3
Case {m,n,p,q}={3,0,1,4}
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http://functions.wolfram.com/07.34.03.0961.01
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MeijerG[{{}, {Subscript[a, 1]}}, {{Subscript[b, 1], Subscript[b, 2],
Subscript[b, 3]}, {Subscript[b, 4]}}, z] ==
((Pi^2 z^Subscript[b, 1] Csc[Pi (-Subscript[b, 1] + Subscript[b, 2])]
Csc[Pi (-Subscript[b, 1] + Subscript[b, 3])])/
Gamma[Subscript[a, 1] - Subscript[b, 1]]) HypergeometricPFQRegularized[
{1 - Subscript[a, 1] + Subscript[b, 1]},
{1 + Subscript[b, 1] - Subscript[b, 2], 1 + Subscript[b, 1] -
Subscript[b, 3], 1 + Subscript[b, 1] - Subscript[b, 4]}, z] +
((Pi^2 z^Subscript[b, 2] Csc[Pi (Subscript[b, 1] - Subscript[b, 2])]
Csc[Pi (-Subscript[b, 2] + Subscript[b, 3])])/
Gamma[Subscript[a, 1] - Subscript[b, 2]]) HypergeometricPFQRegularized[
{1 - Subscript[a, 1] + Subscript[b, 2]},
{1 - Subscript[b, 1] + Subscript[b, 2], 1 + Subscript[b, 2] -
Subscript[b, 3], 1 + Subscript[b, 2] - Subscript[b, 4]}, z] +
((Pi^2 z^Subscript[b, 3] Csc[Pi (Subscript[b, 1] - Subscript[b, 3])]
Csc[Pi (Subscript[b, 2] - Subscript[b, 3])])/
Gamma[Subscript[a, 1] - Subscript[b, 3]]) HypergeometricPFQRegularized[
{1 - Subscript[a, 1] + Subscript[b, 3]},
{1 - Subscript[b, 1] + Subscript[b, 3], 1 - Subscript[b, 2] +
Subscript[b, 3], 1 + Subscript[b, 3] - Subscript[b, 4]}, z] /;
!Element[Subscript[b, 2] - Subscript[b, 1], Integers] &&
!Element[Subscript[b, 3] - Subscript[b, 1], Integers] &&
!Element[Subscript[b, 3] - Subscript[b, 2], Integers]
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</mrow> <mo> + </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 4 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["1", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox[RowBox[List[RowBox[List["-", SubscriptBox["a", "1"]]], "+", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, 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<mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 4 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["1", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", 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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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){kind=small}
