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Hypergeometric Functions
MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z]
Integration
Definite integration
Generalization of classical Meijer's integral from two G functions
Fifteen subgroups for major 39 groups
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http://functions.wolfram.com/07.34.21.0039.01
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Subscript[\[DoubleStruckG], 11] == (Abs[Arg[\[Sigma]]] == SuperStar[b] Pi)
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Cell[BoxData[RowBox[List[SubscriptBox["\[DoubleStruckG]", "11"], "\[Equal]", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", "\[Sigma]", "]"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["b", "*"], "\[Pi]"]]]], ")"]]]]]]
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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> <msub> <mi> 𝕘 </mi> <mn> 11 </mn> </msub> <mo> ⩵ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> σ </mi> <mo> ) </mo> </mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> ⩵ </mo> <mrow> <msup> <mi> b </mi> <mo> * </mo> </msup> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> 𝕘 </ci> <cn type='integer'> 11 </cn> </apply> <apply> <eq /> <apply> <abs /> <apply> <arg /> <ci> σ </ci> </apply> </apply> <apply> <times /> <apply> <ci> SuperStar </ci> <ci> b </ci> </apply> <pi /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SubscriptBox["$Failed", "11"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", "\[Sigma]", "]"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["b", "*"], " ", "\[Pi]"]]]]]]]] |
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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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