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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 > Integrals including G functions with rational arguments





http://functions.wolfram.com/07.34.21.0097.01









  


  










Input Form





Integrate[(\[Tau]^(\[Alpha] - 1)/(\[Tau] + z)^\[Beta]) 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] + z)^k)/\[Tau]^k], {\[Tau], 0, Infinity}] == Sqrt[2 Pi] k^(\[Alpha] - \[Beta]) z^(\[Alpha] - \[Beta]) Gamma[\[Beta] - \[Alpha]] MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, n]}, {Subscript[a, n + 1], \[Ellipsis], Subscript[a, p], \[Beta]/k, \[Ellipsis], (\[Beta] + k - 1)/k}}, {{\[Alpha]/k, \[Ellipsis], (\[Alpha] + k - 1)/k, Subscript[b, 1], \[Ellipsis], Subscript[b, m]}, {Subscript[b, m + 1], \[Ellipsis], Subscript[b, q]}}, \[Omega]] /; Element[k, Integers] && k > 0 && SuperStar[c] > 0 && Abs[Arg[\[Omega]]] < Pi SuperStar[c] && Re[\[Beta] - \[Alpha]] > 0 && k - k Max[Re[Subscript[a, 1]], \[Ellipsis], Re[Subscript[a, n]]] + Re[\[Alpha]] > 0










Standard Form





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MathML Form







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</mo> <mrow> <mo> &#8518; </mo> <mi> &#964; </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <msqrt> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msup> <mi> k </mi> <mrow> <mi> &#945; </mi> <mo> - </mo> <mi> &#946; </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mi> &#945; </mi> <mo> - </mo> <mi> &#946; </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#946; </mi> <mo> - </mo> <mi> &#945; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mrow> <mi> p </mi> <mo> + </mo> <mi> k </mi> </mrow> <mo> , </mo> <mrow> <mi> q </mi> <mo> + </mo> <mi> k </mi> </mrow> </mrow> <mrow> <mrow> <mi> m </mi> <mo> + </mo> <mi> k </mi> </mrow> <mo> , </mo> <mi> n </mi> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#969; </mi> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> &#8230; 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</mo> <mrow> <mrow> <mi> k </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> <mo> &#8743; </mo> <mrow> <msup> <mi> c </mi> <mo> * </mo> </msup> <mo> &gt; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#969; </mi> <mo> ) </mo> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &lt; </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <msup> <mi> c </mi> <mo> * </mo> </msup> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#946; </mi> <mo> - </mo> <mi> &#945; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> k </mi> <mo> - </mo> <mrow> <mi> k </mi> <mo> &#8290; 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Rule Form





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





2001-10-29





© 1998-2014 Wolfram Research, Inc.