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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
Major 39 groups of conditions of convergence of generalization of classical Meijer's integral from two G functions
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http://functions.wolfram.com/07.34.21.0061.01
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Subscript[\[DoubleStruckCapitalC], 18] == (t == 0 && s > 0 &&
SuperStar[b] > 0 && \[Phi] > 0 && Subscript[\[DoubleStruckG], 1] &&
Subscript[\[DoubleStruckG], 2] && Subscript[\[DoubleStruckG], 10])
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Cell[BoxData[RowBox[List[SubscriptBox["\[DoubleStruckCapitalC]", "18"], "\[Equal]", RowBox[List["(", RowBox[List[RowBox[List["t", "\[Equal]", "0"]], "\[And]", RowBox[List["s", ">", "0"]], "\[And]", RowBox[List[SuperscriptBox["b", "*"], ">", "0"]], "\[And]", RowBox[List["\[Phi]", ">", "0"]], "\[And]", SubscriptBox["\[DoubleStruckG]", "1"], "\[And]", SubscriptBox["\[DoubleStruckG]", "2"], "\[And]", SubscriptBox["\[DoubleStruckG]", "10"]]], ")"]]]]]]
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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> ℂ </mi> <mn> 18 </mn> </msub> <mo> ⩵ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> t </mi> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> <mo> ∧ </mo> <mrow> <mi> s </mi> <mo> > </mo> <mn> 0 </mn> </mrow> <mo> ∧ </mo> <mrow> <msup> <mi> b </mi> <mo> * </mo> </msup> <mo> > </mo> <mn> 0 </mn> </mrow> <mo> ∧ </mo> <mrow> <mi> ϕ </mi> <mo> > </mo> <mn> 0 </mn> </mrow> <mo> ∧ </mo> <msub> <mi> 𝕘 </mi> <mn> 1 </mn> </msub> <mo> ∧ </mo> <msub> <mi> 𝕘 </mi> <mn> 2 </mn> </msub> <mo> ∧ </mo> <msub> <mi> 𝕘 </mi> <mn> 10 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> ℂ </ci> <cn type='integer'> 18 </cn> </apply> <apply> <and /> <apply> <eq /> <ci> t </ci> <cn type='integer'> 0 </cn> </apply> <apply> <gt /> <ci> s </ci> <cn type='integer'> 0 </cn> </apply> <apply> <gt /> <apply> <ci> SuperStar </ci> <ci> b </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <gt /> <ci> ϕ </ci> <cn type='integer'> 0 </cn> </apply> <apply> <ci> Subscript </ci> <ci> 𝕘 </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> 𝕘 </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> 𝕘 </ci> <cn type='integer'> 10 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SubscriptBox["$Failed", "18"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["t", "\[Equal]", "0"]], "&&", RowBox[List["s", ">", "0"]], "&&", RowBox[List[SuperscriptBox["b", "*"], ">", "0"]], "&&", RowBox[List["\[Phi]", ">", "0"]], "&&", SubscriptBox["\[DoubleStruckG]", "1"], "&&", SubscriptBox["\[DoubleStruckG]", "2"], "&&", SubscriptBox["\[DoubleStruckG]", "10"]]]]]]] |
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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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