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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/07.34.21.0027.01
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Subscript[\[Lambda], s] ==
Limit[Limit[Subscript[\[Lambda], s0], Arg[\[Sigma]] -> 0, Direction -> -1],
Arg[\[Omega]] -> 0, Direction -> -1]
Limit[Limit[Subscript[\[Lambda], s0], Arg[\[Sigma]] -> 0, Direction -> 1],
Arg[\[Omega]] -> 0, Direction -> -1] /; Arg[\[Sigma]] == 0 &&
Arg[\[Omega]] == 0
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Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[Lambda]", "s"], "\[Equal]", RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List["Limit", "[", RowBox[List[SubscriptBox["\[Lambda]", "s0"], ",", RowBox[List[RowBox[List["Arg", "[", "\[Sigma]", "]"]], "\[Rule]", "0"]], ",", " ", RowBox[List["Direction", " ", "\[Rule]", " ", RowBox[List["-", "1"]]]]]], "]"]], ",", RowBox[List[RowBox[List["Arg", "[", "\[Omega]", "]"]], "\[Rule]", "0"]], ",", " ", RowBox[List["Direction", " ", "\[Rule]", " ", RowBox[List["-", "1"]]]]]], "]"]], RowBox[List["Limit", "[", RowBox[List[RowBox[List["Limit", "[", RowBox[List[SubscriptBox["\[Lambda]", "s0"], ",", RowBox[List[RowBox[List["Arg", "[", "\[Sigma]", "]"]], "\[Rule]", "0"]], ",", " ", RowBox[List["Direction", " ", "\[Rule]", " ", "1"]]]], "]"]], ",", RowBox[List[RowBox[List["Arg", "[", "\[Omega]", "]"]], "\[Rule]", "0"]], ",", " ", RowBox[List["Direction", " ", "\[Rule]", " ", RowBox[List["-", "1"]]]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Arg", "[", "\[Sigma]", "]"]], "\[Equal]", "0"]], "\[And]", RowBox[List[RowBox[List["Arg", "[", "\[Omega]", "]"]], "\[Equal]", "0"]]]]]]]]
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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> <mrow> <msub> <mi> λ </mi> <mi> s </mi> </msub> <mo> ⩵ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <munder> <mi> lim </mi> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> ω </mi> <mo> ) </mo> </mrow> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <msup> <mn> 0 </mn> <mo> + </mo> </msup> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <mrow> <munder> <mi> lim </mi> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> σ </mi> <mo> ) </mo> </mrow> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <msup> <mn> 0 </mn> <mo> + </mo> </msup> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <msub> <mi> λ </mi> <mi> s0 </mi> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <munder> <mi> lim </mi> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> ω </mi> <mo> ) </mo> </mrow> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <msup> <mn> 0 </mn> <mo> + </mo> </msup> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <mrow> <munder> <mi> lim </mi> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> σ </mi> <mo> ) </mo> </mrow> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <msup> <mn> 0 </mn> <mo> - </mo> </msup> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <msub> <mi> λ </mi> <mi> s0 </mi> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> σ </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> ω </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> λ </ci> <ci> s </ci> </apply> <apply> <times /> <apply> <limit /> <bvar> <apply> <arg /> <ci> ω </ci> </apply> </bvar> <condition> <apply> <tendsto type='above' /> <apply> <arg /> <ci> ω </ci> </apply> <cn type='integer'> 0 </cn> </apply> </condition> <apply> <limit /> <bvar> <apply> <arg /> <ci> σ </ci> </apply> </bvar> <condition> <apply> <tendsto type='above' /> <apply> <arg /> <ci> σ </ci> </apply> <cn type='integer'> 0 </cn> </apply> </condition> <apply> <ci> Subscript </ci> <ci> λ </ci> <ci> s0 </ci> </apply> </apply> </apply> <apply> <limit /> <bvar> <apply> <arg /> <ci> ω </ci> </apply> </bvar> <condition> <apply> <tendsto type='above' /> <apply> <arg /> <ci> ω </ci> </apply> <cn type='integer'> 0 </cn> </apply> </condition> <apply> <limit /> <bvar> <apply> <arg /> <ci> σ </ci> </apply> </bvar> <condition> <apply> <tendsto type='below' /> <apply> <arg /> <ci> σ </ci> </apply> <cn type='integer'> 0 </cn> </apply> </condition> <apply> <ci> Subscript </ci> <ci> λ </ci> <ci> s0 </ci> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <eq /> <apply> <arg /> <ci> σ </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <arg /> <ci> ω </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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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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