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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
Notations for conditions of convergence of generalization of classical Meijer's integral from two G functions
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http://functions.wolfram.com/07.34.21.0028.01
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Subscript[\[Lambda], s0] == (q - p) Abs[\[Omega]]^(1/(q - p))
Sign[Arg[\[Omega]]] Sin[\[Psi]] + (v - u) Abs[\[Sigma]]^(1/(v - u))
Sign[Arg[\[Sigma]]] Sin[\[Theta]]
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Cell[BoxData[RowBox[List[SubscriptBox["\[Lambda]", "s0"], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["q", "-", "p"]], ")"]], SuperscriptBox[RowBox[List["Abs", "[", "\[Omega]", "]"]], RowBox[List["1", "/", RowBox[List["(", RowBox[List["q", "-", "p"]], ")"]]]]], RowBox[List["Sign", "[", RowBox[List["Arg", "[", "\[Omega]", "]"]], "]"]], RowBox[List["Sin", "[", "\[Psi]", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["v", "-", "u"]], ")"]], SuperscriptBox[RowBox[List["Abs", "[", "\[Sigma]", "]"]], RowBox[List["1", "/", RowBox[List["(", RowBox[List["v", "-", "u"]], ")"]]]]], RowBox[List["Sign", "[", RowBox[List["Arg", "[", "\[Sigma]", "]"]], "]"]], RowBox[List["Sin", "[", "\[Theta]", "]"]]]]]]]]]]
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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> λ </mi> <mi> s0 </mi> </msub> <mo> ⩵ </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> ω </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> q </mi> <mo> - </mo> <mi> p </mi> </mrow> </mfrac> </msup> <mo> ⁢ </mo> <mrow> <mi> sgn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> ω </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> ψ </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mi> u </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> σ </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> v </mi> <mo> - </mo> <mi> u </mi> </mrow> </mfrac> </msup> <mo> ⁢ </mo> <mrow> <mi> sgn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> σ </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> θ </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> λ </ci> <ci> s0 </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> q </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> <apply> <power /> <apply> <abs /> <ci> ω </ci> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <ci> q </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Sign </ci> <apply> <arg /> <ci> ω </ci> </apply> </apply> <apply> <sin /> <ci> ψ </ci> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> u </ci> </apply> </apply> <apply> <power /> <apply> <abs /> <ci> σ </ci> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> u </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Sign </ci> <apply> <arg /> <ci> σ </ci> </apply> </apply> <apply> <sin /> <ci> θ </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SubscriptBox["$Failed", "s0_"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["q", "-", "p"]], ")"]], " ", SuperscriptBox[RowBox[List["Abs", "[", "\[Omega]", "]"]], FractionBox["1", RowBox[List["q", "-", "p"]]]], " ", RowBox[List["Sign", "[", RowBox[List["Arg", "[", "\[Omega]", "]"]], "]"]], " ", RowBox[List["Sin", "[", "\[Psi]", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["v", "-", "u"]], ")"]], " ", SuperscriptBox[RowBox[List["Abs", "[", "\[Sigma]", "]"]], FractionBox["1", RowBox[List["v", "-", "u"]]]], " ", RowBox[List["Sign", "[", RowBox[List["Arg", "[", "\[Sigma]", "]"]], "]"]], " ", RowBox[List["Sin", "[", "\[Theta]", "]"]]]]]]]]]] |
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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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