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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}={3,1,2,4}
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http://functions.wolfram.com/07.34.03.0988.01
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MeijerG[{{Subscript[a, 1]}, {Subscript[a, 2]}},
{{Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, {Subscript[b, 4]}},
z] == ((Pi^2 Csc[Pi (-Subscript[b, 1] + Subscript[b, 2])]
Csc[Pi (-Subscript[b, 1] + Subscript[b, 3])]
Gamma[1 - Subscript[a, 1] + Subscript[b, 1]])/
Gamma[Subscript[a, 2] - Subscript[b, 1]]) z^Subscript[b, 1]
HypergeometricPFQRegularized[{1 - Subscript[a, 1] + Subscript[b, 1],
1 - Subscript[a, 2] + 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 Csc[Pi (Subscript[b, 1] - Subscript[b, 2])]
Csc[Pi (-Subscript[b, 2] + Subscript[b, 3])]
Gamma[1 - Subscript[a, 1] + Subscript[b, 2]])/
Gamma[Subscript[a, 2] - Subscript[b, 2]]) z^Subscript[b, 2]
HypergeometricPFQRegularized[{1 - Subscript[a, 1] + Subscript[b, 2],
1 - Subscript[a, 2] + 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 Csc[Pi (Subscript[b, 1] - Subscript[b, 3])]
Csc[Pi (Subscript[b, 2] - Subscript[b, 3])]
Gamma[1 - Subscript[a, 1] + Subscript[b, 3]])/
Gamma[Subscript[a, 2] - Subscript[b, 3]]) z^Subscript[b, 3]
HypergeometricPFQRegularized[{1 - Subscript[a, 1] + Subscript[b, 3],
1 - Subscript[a, 2] + 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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<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> <mn> 2 </mn> <mo> , </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 3 </mn> <mo> , </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mtable> <mtr> <mtd> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <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> <mo> , </mo> <msub> <mi> b </mi> <mn> 4 </mn> </msub> </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", ",", "1"]]], 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<mrow> <mrow> <mrow> <mo> - </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ; </mo> <mrow> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </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> 1 </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]", 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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}
