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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 > Integral from three G functions





http://functions.wolfram.com/07.34.21.0081.01









  


  








Input Form





Integrate[t^(\[Alpha] - 1) 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]}}, t z] MeijerG[{{Subscript[a, 11], \[Ellipsis], Subscript[a, 1 Subscript[n, 1]]}, {Subscript[a, 1 Subscript[n, 1] + 1], \[Ellipsis], Subscript[a, 1 Subscript[p, 1]]}}, {{Subscript[b, 11], \[Ellipsis], Subscript[b, 1 Subscript[m, 1]]}, {Subscript[b, 1 Subscript[m, 1] + 1], \[Ellipsis], Subscript[b, 1 Subscript[q, 1]]}}, t x] MeijerG[{{Subscript[a, 21], \[Ellipsis], Subscript[a, 2 Subscript[n, 2]]}, {Subscript[a, 2 Subscript[n, 2] + 1], \[Ellipsis], Subscript[a, 2 Subscript[p, 2]]}}, {{Subscript[b, 21], \[Ellipsis], Subscript[b, 2 Subscript[m, 2]]}, {Subscript[b, 2 Subscript[m, 2] + 1], \[Ellipsis], Subscript[b, 2 Subscript[q, 2]]}}, t y], {t, 0, Infinity}] == MeijerG[{{{1 - \[Alpha] - Subscript[b, 1], \[Ellipsis], 1 - \[Alpha] - Subscript[b, m]}, {1 - \[Alpha] - Subscript[b, m + 1], \[Ellipsis], 1 - \[Alpha] - Subscript[b, q]}}, {{1 - \[Alpha] - Subscript[a, 1], \[Ellipsis], 1 - \[Alpha] - Subscript[a, n]}, {1 - \[Alpha] - Subscript[a, n + 1], \[Ellipsis], 1 - \[Alpha] - Subscript[a, p]}}}, {{{Subscript[a, 11], \[Ellipsis], Subscript[a, 1 Subscript[n, 1]]}, {Subscript[a, 1 Subscript[n, 1] + 1], \[Ellipsis], Subscript[a, 1 Subscript[p, 1]]}}, {{Subscript[b, 11], \[Ellipsis], Subscript[b, 1 Subscript[m, 1]]}, {Subscript[b, 1 Subscript[m, 1] + 1], \[Ellipsis], Subscript[b, 1 Subscript[q, 1]]}}}, {{{Subscript[a, 21], \[Ellipsis], Subscript[a, 2 Subscript[n, 2]]}, {Subscript[a, 2 Subscript[n, 2] + 1], \[Ellipsis], Subscript[a, 2 Subscript[p, 2]]}}, {{Subscript[b, 21], \[Ellipsis], Subscript[b, 2 Subscript[m, 2]]}, {Subscript[b, 2 Subscript[m, 2] + 1], \[Ellipsis], Subscript[b, 2 Subscript[q, 2]]}}}, x/z, y/z]/z^\[Alpha]








Standard Form





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MathML Form







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</ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> GridBox </ci> <list> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> 11 </ms> </apply> <ms> , </ms> </list> </apply> </list> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <ms> 11 </ms> </apply> <ms> , </ms> </list> </apply> </list> </list> </apply> <apply> <ci> GridBox </ci> <list> <list> <apply> <ci> RowBox </ci> <list> <ms> &#8230; </ms> <ms> , </ms> </list> </apply> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <apply> <ci> SubscriptBox </ci> <ms> p </ms> <ms> 1 </ms> </apply> </list> </apply> </apply> </list> <list> <apply> <ci> RowBox </ci> <list> <ms> &#8230; </ms> <ms> , </ms> </list> </apply> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <apply> <ci> SubscriptBox </ci> <ms> q </ms> <ms> 1 </ms> </apply> </list> </apply> </apply> </list> </list> </apply> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubsuperscriptBox </ci> <ms> G </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> p </ms> <ms> 2 </ms> </apply> <ms> , </ms> <apply> <ci> SubscriptBox </ci> <ms> q </ms> <ms> 2 </ms> </apply> </list> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> m </ms> <ms> 2 </ms> </apply> <ms> , </ms> <apply> <ci> SubscriptBox </ci> <ms> n </ms> <ms> 2 </ms> </apply> </list> </apply> </apply> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> y </ms> <ms> t </ms> </list> </apply> <ms> &#10072; 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</ms> <ms> - </ms> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <ms> 1 </ms> </apply> </list> </apply> <ms> , </ms> </list> </apply> </list> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> - </ms> <ms> &#945; </ms> <ms> - </ms> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> 1 </ms> </apply> </list> </apply> <ms> , </ms> </list> </apply> </list> </list> </apply> <apply> <ci> GridBox </ci> <list> <list> <apply> <ci> RowBox </ci> <list> <ms> &#8230; </ms> <ms> , </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> - </ms> <ms> &#945; </ms> <ms> - </ms> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <ms> q </ms> </apply> </list> </apply> </list> <list> <apply> <ci> RowBox </ci> <list> <ms> &#8230; </ms> <ms> , </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> - </ms> <ms> &#945; </ms> <ms> - </ms> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> p </ms> </apply> </list> </apply> </list> </list> </apply> </list> </apply> <ms> &#10072; 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Rule Form





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





2001-10-29