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variants of this functions
MeijerG






Mathematica Notation

Traditional Notation









Hypergeometric Functions > MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z] > Integration > Definite integration > Classical Meijer's integral from two G functions





http://functions.wolfram.com/07.34.21.0011.01









  


  










Input Form





Integrate[\[Tau]^(\[Alpha] - 1) MeijerG[{{Subscript[c, 1], \[Ellipsis], Subscript[c, t]}, {Subscript[c, t + 1], \[Ellipsis], Subscript[c, u]}}, {{Subscript[d, 1], \[Ellipsis], Subscript[d, s]}, {Subscript[d, s + 1], \[Ellipsis], Subscript[d, v]}}, \[Tau] w] MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, n]}, {Subscript[a, n + 1], \[Ellipsis], Subscript[a, p]}}, {{Subscript[b, 1], \[Ellipsis], Subscript[b, m]}, {Subscript[b, m + 1], \[Ellipsis], Subscript[b, q]}}, \[Tau] z], {\[Tau], 0, Infinity}] == MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, n], 1 - \[Alpha] - Subscript[d, 1], \[Ellipsis], 1 - \[Alpha] - Subscript[d, s]}, {1 - \[Alpha] - Subscript[d, s + 1], \[Ellipsis], 1 - \[Alpha] - Subscript[d, v], Subscript[a, n + 1], \[Ellipsis], Subscript[a, p]}}, {{Subscript[b, 1], \[Ellipsis], Subscript[b, m], 1 - \[Alpha] - Subscript[c, 1], \[Ellipsis], 1 - \[Alpha] - Subscript[c, t]}, {1 - \[Alpha] - Subscript[c, t + 1], \[Ellipsis], 1 - \[Alpha] - Subscript[c, u], Subscript[b, m + 1], \[Ellipsis], Subscript[b, q]}}, z/w]/w^\[Alpha] /; (\[DoubleStruckCapitalC]\[DoubleStruckCapitalC] /; k == l == 1)










Standard Form





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MathML Form







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</mo> <mrow> <mo> ( </mo> <mrow> <mi> &#8450;&#8450; </mi> <mo> /; </mo> <mrow> <mi> k </mi> <mo> &#10869; </mo> <mi> l </mi> <mo> &#10869; </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <msubsup> <mo> &#8747; </mo> <mn> 0 </mn> <mi> &#8734; </mi> </msubsup> <mrow> <mrow> <msup> <mi> &#964; </mi> <mrow> <mi> &#945; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mi> u </mi> <mo> , </mo> <mi> v </mi> </mrow> <mrow> <mi> s </mi> <mo> , </mo> <mi> t </mi> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#964; </mi> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <msub> <mi> c </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> c </mi> <mi> t </mi> </msub> <mo> , </mo> <msub> <mi> c </mi> <mrow> <mi> t </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> &#8230; 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</mi> <mo> - </mo> <msub> <mi> d </mi> <mrow> <mi> s </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> &#8290; </mo> <mrow> <mrow> <mo> - </mo> <mi> &#945; </mi> </mrow> <mo> - </mo> <msub> <mi> d </mi> <mi> v </mi> </msub> </mrow> </mrow> <mo> , </mo> <msub> <mi> a </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> a </mi> <mi> p </mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> b </mi> <mi> m </mi> </msub> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> c </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> c </mi> <mi> t </mi> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#945; </mi> <mo> - </mo> <msub> <mi> c </mi> <mrow> <mi> t </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> &#8290; </mo> <mrow> <mrow> <mo> - </mo> <mi> &#945; </mi> </mrow> <mo> - </mo> <msub> <mi> c </mi> <mi> u </mi> </msub> </mrow> </mrow> <mo> , </mo> <msub> <mi> b </mi> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> b </mi> <mi> q </mi> </msub> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[RowBox[List[&quot;v&quot;, &quot;+&quot;, &quot;p&quot;]], &quot;,&quot;, RowBox[List[&quot;u&quot;, &quot;+&quot;, &quot;q&quot;]]]], RowBox[List[RowBox[List[&quot;m&quot;, &quot;+&quot;, &quot;t&quot;]], &quot;,&quot;, RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;s&quot;]]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[FractionBox[&quot;z&quot;, &quot;w&quot;], MeijerG, Rule[Editable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[SubscriptBox[&quot;a&quot;, &quot;1&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;a&quot;, &quot;n&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, &quot;\[Alpha]&quot;, &quot;-&quot;, SubscriptBox[&quot;d&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, &quot;\[Alpha]&quot;, &quot;-&quot;, SubscriptBox[&quot;d&quot;, &quot;s&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, &quot;\[Alpha]&quot;, &quot;-&quot;, SubscriptBox[&quot;d&quot;, RowBox[List[&quot;s&quot;, &quot;+&quot;, &quot;1&quot;]]]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, RowBox[List[&quot;1&quot;, TagBox[RowBox[List[RowBox[List[&quot;-&quot;, &quot;\[Alpha]&quot;]], &quot;-&quot;, SubscriptBox[&quot;d&quot;, &quot;v&quot;]]], MeijerG, Rule[Editable, True]]]], &quot;,&quot;, TagBox[SubscriptBox[&quot;a&quot;, RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;a&quot;, &quot;p&quot;], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[SubscriptBox[&quot;b&quot;, &quot;1&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;b&quot;, &quot;m&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, &quot;\[Alpha]&quot;, &quot;-&quot;, SubscriptBox[&quot;c&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, &quot;\[Alpha]&quot;, &quot;-&quot;, SubscriptBox[&quot;c&quot;, &quot;t&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, &quot;\[Alpha]&quot;, &quot;-&quot;, SubscriptBox[&quot;c&quot;, RowBox[List[&quot;t&quot;, &quot;+&quot;, &quot;1&quot;]]]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, RowBox[List[&quot;1&quot;, TagBox[RowBox[List[RowBox[List[&quot;-&quot;, &quot;\[Alpha]&quot;]], &quot;-&quot;, SubscriptBox[&quot;c&quot;, &quot;u&quot;]]], MeijerG, Rule[Editable, True]]]], &quot;,&quot;, TagBox[SubscriptBox[&quot;b&quot;, RowBox[List[&quot;m&quot;, &quot;+&quot;, &quot;1&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;b&quot;, &quot;q&quot;], MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, True]] </annotation> </semantics> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#8450;&#8450; </mi> <mo> /; </mo> <mrow> <mi> k </mi> <mo> &#10869; </mo> <mi> l </mi> <mo> &#10869; </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29





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