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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 for classical integral transforms





http://functions.wolfram.com/07.34.21.0085.01









  


  










Input Form





Integrate[\[Tau]^(\[Alpha] - 1) (\[Tau] - a)^(\[Beta] - 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]}}, \[Omega] \[Tau]^(l/k)], {\[Tau], a, Infinity}] == ((k^\[Mu] Gamma[\[Beta]])/(l^\[Beta] ((2 Pi)^(SuperStar[c] (k - 1)) a^(1 - \[Alpha] - \[Beta])))) MeijerG[{{Subscript[a, 1]/k, \[Ellipsis], (Subscript[a, 1] + k - 1)/k, \[Ellipsis], Subscript[a, n]/k, \[Ellipsis], (Subscript[a, n] + k - 1)/ k}, {Subscript[a, n + 1]/k, \[Ellipsis], (Subscript[a, n + 1] + k - 1)/ k, \[Ellipsis], Subscript[a, p]/k, \[Ellipsis], (Subscript[a, p] + k - 1)/k, (1 - \[Alpha])/l, \[Ellipsis], (l - \[Alpha])/l}}, {{(1 - \[Alpha] - \[Beta])/l, \[Ellipsis], (l - \[Alpha] - \[Beta])/l, Subscript[b, 1]/k, \[Ellipsis], (Subscript[b, 1] + k - 1)/k, \[Ellipsis], Subscript[b, m]/k, \[Ellipsis], (Subscript[b, m] + k - 1)/k}, {Subscript[b, m + 1]/k, \[Ellipsis], (Subscript[b, m + 1] + k - 1)/k, \[Ellipsis], Subscript[b, q]/k, \[Ellipsis], (Subscript[b, q] + k - 1)/k}}, (\[Omega]^k a^l)/k^(k (q - p))] /; Element[k, Integers] && k > 0 && Element[l, Integers] && l > 0 && GCD[k, l] == 1 && (\[DoubleStruckCapitalC]\[DoubleStruckCapitalC] /; \[Sigma] == a^(-1) && t == u == v == 1 && s == Subscript[d, 1] == 0 && Subscript[c, 1] == \[Beta])










Standard Form





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MathML Form







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&quot;-&quot;, &quot;\[Alpha]&quot;, &quot;-&quot;, &quot;\[Beta]&quot;]], &quot;l&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[SubscriptBox[&quot;b&quot;, &quot;1&quot;], &quot;k&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[SubscriptBox[&quot;b&quot;, &quot;1&quot;], &quot;+&quot;, &quot;k&quot;, &quot;-&quot;, &quot;1&quot;]], &quot;k&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[SubscriptBox[&quot;b&quot;, &quot;m&quot;], &quot;k&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[SubscriptBox[&quot;b&quot;, &quot;m&quot;], &quot;+&quot;, &quot;k&quot;, &quot;-&quot;, &quot;1&quot;]], &quot;k&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[SubscriptBox[&quot;b&quot;, RowBox[List[&quot;m&quot;, &quot;+&quot;, &quot;1&quot;]]], &quot;k&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[SubscriptBox[&quot;b&quot;, RowBox[List[&quot;m&quot;, &quot;+&quot;, &quot;1&quot;]]], &quot;+&quot;, &quot;k&quot;, &quot;-&quot;, &quot;1&quot;]], &quot;k&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[SubscriptBox[&quot;b&quot;, &quot;q&quot;], &quot;k&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[SubscriptBox[&quot;b&quot;, &quot;q&quot;], &quot;+&quot;, &quot;k&quot;, &quot;-&quot;, &quot;1&quot;]], &quot;k&quot;], MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, True]] </annotation> </semantics> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> k </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> <mo> &#8743; </mo> <mrow> <mi> l </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> k </mi> <mo> , </mo> <mi> l </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#8450;&#8450; </mi> <mo> /; </mo> <mrow> <mrow> <mi> &#963; </mi> <mo> &#10869; </mo> <mfrac> <mn> 1 </mn> <mi> a </mi> </mfrac> </mrow> <mo> &#8743; </mo> <mrow> <mi> t </mi> <mo> &#10869; </mo> <mi> u </mi> <mo> &#10869; </mo> <mi> v </mi> <mo> &#10869; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> s </mi> <mo> &#10869; </mo> <msub> <mi> d </mi> <mn> 1 </mn> </msub> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> c </mi> <mn> 1 </mn> </msub> <mo> &#10869; </mo> <mi> &#946; </mi> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29