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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/07.34.21.0033.01
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Subscript[\[DoubleStruckG], 5] ==
((p - q) Re[\[Alpha] + Subscript[d, h]] - r Re[\[Mu]] > -((3 r)/2) /;
1 <= h <= s)
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Cell[BoxData[RowBox[List[SubscriptBox["\[DoubleStruckG]", "5"], "\[Equal]", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["p", "-", "q"]], ")"]], RowBox[List["Re", "[", RowBox[List["\[Alpha]", "+", SubscriptBox["d", "h"]]], "]"]]]], "-", RowBox[List["r", " ", RowBox[List["Re", "[", "\[Mu]", "]"]]]]]], ">", RowBox[List["-", FractionBox[RowBox[List["3", "r"]], "2"]]]]], "/;", RowBox[List["1", "\[LessEqual]", "h", "\[LessEqual]", "s"]]]], ")"]]]]]]
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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> 5 </mn> </msub> <mo> ⩵ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> p </mi> <mo> - </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> α </mi> <mo> + </mo> <msub> <mi> d </mi> <mi> h </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> r </mi> <mo> ⁢ </mo> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> μ </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> > </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> /; </mo> <mrow> <mn> 1 </mn> <mo> ≤ </mo> <mi> h </mi> <mo> ≤ </mo> <mi> s </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> 𝕘 </ci> <cn type='integer'> 5 </cn> </apply> <apply> <ci> Condition </ci> <apply> <gt /> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> </apply> <apply> <real /> <apply> <plus /> <ci> α </ci> <apply> <ci> Subscript </ci> <ci> d </ci> <ci> h </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> r </ci> <apply> <real /> <ci> μ </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <ci> r </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <leq /> <cn type='integer'> 1 </cn> <ci> h </ci> <ci> s </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SubscriptBox["$Failed", "5"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["p", "-", "q"]], ")"]], " ", RowBox[List["Re", "[", RowBox[List["\[Alpha]", "+", SubscriptBox["d", "h"]]], "]"]]]], "-", RowBox[List["r", " ", RowBox[List["Re", "[", "\[Mu]", "]"]]]]]], ">", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["3", " ", "r"]], ")"]]]]]], "/;", RowBox[List["1", "\[LessEqual]", "h", "\[LessEqual]", "s"]]]]]]]] |
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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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