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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/07.34.21.0079.01
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Subscript[\[DoubleStruckCapitalC], 35] == (m == \[Phi] == 0 && u > v + 1 &&
n > 0 && SuperStar[c] > 0 && SuperStar[b] >= 0 &&
SuperStar[b] Pi < Abs[Arg[\[Sigma]]] < (s + t - v + 1) Pi &&
Subscript[\[DoubleStruckG], 1] && Subscript[\[DoubleStruckG], 3] &&
Subscript[\[DoubleStruckG], 12] && Subscript[\[DoubleStruckG], 14] &&
Subscript[\[DoubleStruckG], 15])
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Cell[BoxData[RowBox[List[SubscriptBox["\[DoubleStruckCapitalC]", "35"], "\[Equal]", RowBox[List["(", RowBox[List[RowBox[List["m", "\[Equal]", "\[Phi]", "\[Equal]", "0"]], "\[And]", RowBox[List["u", ">", RowBox[List["v", "+", "1"]]]], "\[And]", RowBox[List["n", ">", "0"]], "\[And]", RowBox[List[SuperscriptBox["c", "*"], ">", "0"]], "\[And]", RowBox[List[SuperscriptBox["b", "*"], "\[GreaterEqual]", "0"]], "\[And]", RowBox[List[RowBox[List[SuperscriptBox["b", "*"], "\[Pi]"]], "<", RowBox[List["Abs", "[", RowBox[List["Arg", "[", "\[Sigma]", "]"]], "]"]], "<", RowBox[List[RowBox[List["(", RowBox[List["s", "+", "t", "-", "v", "+", "1"]], ")"]], "\[Pi]"]]]], "\[And]", SubscriptBox["\[DoubleStruckG]", "1"], "\[And]", SubscriptBox["\[DoubleStruckG]", "3"], "\[And]", SubscriptBox["\[DoubleStruckG]", "12"], "\[And]", SubscriptBox["\[DoubleStruckG]", "14"], "\[And]", SubscriptBox["\[DoubleStruckG]", "15"]]], ")"]]]]]]
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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> 35 </mn> </msub> <mo> ⩵ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> m </mi> <mo> ⩵ </mo> <mi> ϕ </mi> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> <mo> ∧ </mo> <mrow> <mi> u </mi> <mo> > </mo> <mrow> <mi> v </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ∧ </mo> <mrow> <mi> n </mi> <mo> > </mo> <mn> 0 </mn> </mrow> <mo> ∧ </mo> <mrow> <msup> <mi> c </mi> <mo> * </mo> </msup> <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> <mrow> <msup> <mi> b </mi> <mo> * </mo> </msup> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> < </mo> <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> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> + </mo> <mi> t </mi> <mo> - </mo> <mi> v </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mrow> <mo> ∧ </mo> <msub> <mi> 𝕘 </mi> <mn> 1 </mn> </msub> <mo> ∧ </mo> <msub> <mi> 𝕘 </mi> <mn> 3 </mn> </msub> <mo> ∧ </mo> <msub> <mi> 𝕘 </mi> <mn> 12 </mn> </msub> <mo> ∧ </mo> <msub> <mi> 𝕘 </mi> <mn> 14 </mn> </msub> <mo> ∧ </mo> <msub> <mi> 𝕘 </mi> <mn> 15 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> ℂ </ci> <cn type='integer'> 35 </cn> </apply> <apply> <and /> <apply> <eq /> <ci> m </ci> <ci> ϕ </ci> <cn type='integer'> 0 </cn> </apply> <apply> <gt /> <ci> u </ci> <apply> <plus /> <ci> v </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <gt /> <ci> n </ci> <cn type='integer'> 0 </cn> </apply> <apply> <gt /> <apply> <ci> SuperStar </ci> <ci> c </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <geq /> <apply> <ci> SuperStar </ci> <ci> b </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <lt /> <apply> <times /> <apply> <ci> SuperStar </ci> <ci> b </ci> </apply> <pi /> </apply> <apply> <abs /> <apply> <arg /> <ci> σ </ci> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> s </ci> <ci> t </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> v </ci> </apply> <cn type='integer'> 1 </cn> </apply> <pi /> </apply> </apply> <apply> <ci> Subscript </ci> <ci> 𝕘 </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> 𝕘 </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> 𝕘 </ci> <cn type='integer'> 12 </cn> </apply> <apply> <ci> Subscript </ci> <ci> 𝕘 </ci> <cn type='integer'> 14 </cn> </apply> <apply> <ci> Subscript </ci> <ci> 𝕘 </ci> <cn type='integer'> 15 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SubscriptBox["$Failed", "35"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["m", "\[Equal]", "\[Phi]", "\[Equal]", "0"]], "&&", RowBox[List["u", ">", RowBox[List["v", "+", "1"]]]], "&&", RowBox[List["n", ">", "0"]], "&&", RowBox[List[SuperscriptBox["c", "*"], ">", "0"]], "&&", RowBox[List[SuperscriptBox["b", "*"], "\[GreaterEqual]", "0"]], "&&", RowBox[List[RowBox[List[SuperscriptBox["b", "*"], " ", "\[Pi]"]], "<", RowBox[List["Abs", "[", RowBox[List["Arg", "[", "\[Sigma]", "]"]], "]"]], "<", RowBox[List[RowBox[List["(", RowBox[List["s", "+", "t", "-", "v", "+", "1"]], ")"]], " ", "\[Pi]"]]]], "&&", SubscriptBox["\[DoubleStruckG]", "1"], "&&", SubscriptBox["\[DoubleStruckG]", "3"], "&&", SubscriptBox["\[DoubleStruckG]", "12"], "&&", SubscriptBox["\[DoubleStruckG]", "14"], "&&", SubscriptBox["\[DoubleStruckG]", "15"]]]]]]] |
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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}
