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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] > Specific values > Specialized values > Cases with arbitrary {m,n,p,q} > Case {m,n,p,q}={1,p,p,q}





http://functions.wolfram.com/07.34.03.0016.01









  


  










Input Form





MeijerG[{{0, (Subscript[a, 1] - m)/n, (Subscript[a, 1] - m + 1)/n, \[Ellipsis], (Subscript[a, 1] - m + n - 1)/n, \[Ellipsis], (Subscript[a, p] - m)/n, (Subscript[a, p] - m + 1)/n, \[Ellipsis], (Subscript[a, p] - m + n - 1)/n}, {}}, {{0}, {-(m/n), (-m + 1)/n, \[Ellipsis], (-m + n - 1)/n, (Subscript[b, 1] - m)/n, (Subscript[b, 1] - m + 1)/n, \[Ellipsis], (Subscript[b, 1] - m + n - 1)/n, \[Ellipsis], (Subscript[b, q] - m)/n, (Subscript[b, q] - m + 1)/n, \[Ellipsis], (Subscript[b, q] - m + n - 1)/ n}}, z] == ((2 Pi)^((q - p + 1) ((1 - n)/2)) n^((1/2) (-1 - p + q) + Sum[Subscript[a, j], {j, 1, p}] - Sum[Subscript[b, j], {j, 1, q}]) (Product[Gamma[1 - Subscript[a, j]], {j, 1, p}]/Product[Gamma[1 - Subscript[b, j]], {j, 1, q}]) Sum[Exp[-((2 Pi I k m)/n)] HypergeometricPFQ[{1 - Subscript[a, 1], \[Ellipsis], 1 - Subscript[a, p]}, {1 - Subscript[b, 1], \[Ellipsis], 1 - Subscript[b, q]}, n^(q - p + 1) Exp[(2 Pi I k)/n] (-z)^(1/n)], {k, 0, n - 1}])/(-z)^(m/n) /; Element[m, Integers] && m > 0 && Element[n, Integers] && n > 0










Standard Form





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MathML Form







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</mo> <mrow> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <mi> p </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> q </mi> </munderover> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <msup> <mi> n </mi> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <mi> p </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <munderover> <mo> &#8721; 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Date Added to functions.wolfram.com (modification date)





2001-10-29