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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/07.34.21.0092.01









  


  










Input Form





Integrate[\[Tau]^(\[Alpha] - 1) BesselY[\[Nu], b \[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]^((2 l)/k)], {\[Tau], 0, Infinity}] == ((k^\[Mu] (2 l)^(\[Alpha] - 1))/(b^\[Alpha] (2 Pi)^(SuperStar[c] (k - 1)))) MeijerG[{{(1 - (\[Alpha] + \[Nu])/2)/l, \[Ellipsis], (l - (\[Alpha] + \[Nu])/2)/l, (1 - (\[Alpha] - \[Nu])/2)/l, \[Ellipsis], (l - (\[Alpha] - \[Nu])/2)/l, 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, (3 - \[Alpha] + \[Nu])/(2 l), \[Ellipsis], ((1 - \[Alpha] + \[Nu])/2 + l)/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, (3 - \[Alpha] + \[Nu])/(2 l), \[Ellipsis], ((1 - \[Alpha] + \[Nu])/2 + l)/l}}, (\[Omega]^k (2 l)^(2 l))/ (b^(2 l) k^(k (q - p)))] /; Element[k, Integers] && k > 0 && Element[l, Integers] && l > 0 && GCD[k, l] == 1 && (\[DoubleStruckCapitalC]\[DoubleStruckCapitalC] /; \[Alpha] -> \[Alpha]/2 && \[Sigma] == b^2/4 && s == 2 && t == 0 && u == 1 && v == 3 && Subscript[c, 1] == Subscript[d, 3] == (1 - \[Nu])/2 && Subscript[d, 1] == -(\[Nu]/2) && Subscript[d, 2] == \[Nu]/2)










Standard Form





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MathML Form







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&#8290; </mo> <mi> l </mi> </mrow> </mrow> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <msup> <mi> &#969; </mi> <mi> k </mi> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> l </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> l </mi> </mrow> </msup> </mrow> <mrow> <msup> <mi> b </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> l </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> k </mi> <mrow> <mi> k </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> </mrow> </mfrac> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mrow> <mi> &#945; </mi> <mo> + </mo> <mi> &#957; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mi> l </mi> <mo> - </mo> <mfrac> <mrow> <mi> &#945; </mi> <mo> + </mo> <mi> &#957; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mrow> <mi> &#945; </mi> <mo> - </mo> <mi> &#957; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <mi> l </mi> <mo> - </mo> <mfrac> <mrow> <mi> &#945; </mi> <mo> - </mo> <mi> &#957; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mi> l </mi> </mfrac> <mo> , </mo> <mfrac> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mi> k </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mi> k </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <msub> <mi> a </mi> <mi> n </mi> </msub> <mi> k </mi> </mfrac> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mfrac> <mrow> <msub> <mi> a </mi> <mi> n </mi> </msub> <mo> + </mo> <mi> k </mi> <mo> 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</mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#8450;&#8450; </mi> <mo> /; </mo> <mi> &#945; </mi> </mrow> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mrow> <mfrac> <mi> &#945; </mi> <mn> 2 </mn> </mfrac> <mo> &#8743; </mo> <mrow> <mi> &#963; </mi> <mo> &#10869; </mo> <mfrac> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mn> 4 </mn> </mfrac> </mrow> <mo> &#8743; </mo> <mrow> <mi> s </mi> <mo> &#10869; </mo> <mn> 2 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> t </mi> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> u </mi> <mo> &#10869; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> v </mi> <mo> &#10869; </mo> <mn> 3 </mn> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> c </mi> <mn> 1 </mn> </msub> <mo> &#10869; </mo> <msub> <mi> d </mi> <mn> 3 </mn> </msub> <mo> &#10869; </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#957; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> d </mi> <mn> 1 </mn> </msub> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mfrac> <mi> &#957; </mi> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> d </mi> <mn> 2 </mn> </msub> <mo> &#10869; </mo> <mfrac> <mi> &#957; </mi> <mn> 2 </mn> </mfrac> </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