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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 > Generalization of classical Meijer's integral from two G functions > Main formulas





http://functions.wolfram.com/07.34.21.0012.01









  


  








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]}}, \[Sigma] \[Tau]] 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]}}, \[Omega] \[Tau]^r], {\[Tau], 0, Infinity}] == FoxH[{{{Subscript[a, 1], Subscript[A, 1]}, \[Ellipsis], {Subscript[a, n], Subscript[A, n]}}, {{Subscript[a, n + 1], Subscript[A, n + 1]}, \[Ellipsis], {Subscript[a, p], Subscript[A, p]}}}, {{{Subscript[b, 1], Subscript[B, 1]}, \[Ellipsis], {Subscript[b, m], Subscript[B, m]}}, {{Subscript[b, m + 1], Subscript[B, m + 1]}, \[Ellipsis], {Subscript[b, q], Subscript[B, q]}}}, \[Omega]/\[Sigma]^r]/ \[Sigma]^\[Alpha] /; r > 0








Standard Form





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MathML Form







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</ms> <ms> , </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <ms> m </ms> </apply> <ms> , </ms> <ms> 1 </ms> </list> </apply> <ms> ) </ms> </list> </apply> <ms> , </ms> </list> </apply> </list> </list> </apply> <apply> <ci> GridBox </ci> <list> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <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> d </ms> <ms> 1 </ms> </apply> </list> </apply> <ms> , </ms> <ms> r </ms> </list> </apply> <ms> ) </ms> </list> </apply> <ms> , </ms> </list> </apply> </list> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <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> c </ms> <ms> 1 </ms> </apply> </list> </apply> <ms> , </ms> <ms> r </ms> </list> </apply> <ms> ) </ms> </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> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <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> d </ms> <ms> v </ms> </apply> </list> </apply> <ms> , </ms> <ms> r </ms> </list> </apply> <ms> ) </ms> </list> </apply> <ms> , </ms> </list> </apply> </list> <list> <apply> <ci> RowBox </ci> <list> <ms> &#8230; </ms> <ms> , </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <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> c </ms> <ms> u </ms> </apply> </list> </apply> <ms> , </ms> <ms> r </ms> </list> </apply> <ms> ) </ms> </list> </apply> <ms> , </ms> </list> </apply> </list> </list> </apply> <apply> <ci> GridBox </ci> <list> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <apply> <ci> RowBox </ci> <list> <ms> n </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> </apply> <ms> , </ms> <ms> 1 </ms> </list> </apply> <ms> ) </ms> </list> </apply> <ms> , </ms> </list> </apply> </list> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <apply> <ci> RowBox </ci> <list> <ms> m </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> </apply> <ms> , </ms> <ms> 1 </ms> </list> </apply> <ms> ) </ms> </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> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> p </ms> </apply> <ms> , </ms> <ms> 1 </ms> </list> </apply> <ms> ) </ms> </list> </apply> </list> <list> <apply> <ci> RowBox </ci> <list> <ms> &#8230; </ms> <ms> , </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <ms> q </ms> </apply> <ms> , </ms> <ms> 1 </ms> </list> </apply> <ms> ) </ms> </list> </apply> </list> </list> </apply> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <ms> . </ms> </list> </apply> </list> </apply> </list> </apply> <ms> /; </ms> <apply> <ci> RowBox </ci> <list> <ms> r </ms> <ms> &gt; </ms> <ms> 0 </ms> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29