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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/07.34.03.0009.01









  


  










Input Form





MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {}}, {{0}, {Subscript[a, 1] - Subscript[m, 1], \[Ellipsis], Subscript[a, n] - Subscript[m, n], Subscript[b, n + 1], \[Ellipsis], Subscript[b, q]}}, z] == (Product[Gamma[1 - Subscript[a, j]], {j, n + 1, p}]/ (Product[(Subscript[m, j] - 1)!, {j, 1, n}] Product[Gamma[1 - Subscript[b, j]], {j, n + 1, q}])) Sum[\[Ellipsis] Sum[(1/(1 - Subscript[a, k] + Subscript[j, k])) Product[(Pochhammer[1 - Subscript[m, l], Subscript[j, l]]/ Subscript[j, l]!) Product[If[i == k, 1, 1/(Subscript[a, k] + Subscript[j, i] - Subscript[a, i] - Subscript[j, k])] HypergeometricPFQ[{1 - Subscript[a, k] + Subscript[j, k], 1 - Subscript[a, n + 1], \[Ellipsis], 1 - Subscript[a, p]}, {2 - Subscript[a, k] + Subscript[j, k], 1 - Subscript[b, n + 1], \[Ellipsis], 1 - Subscript[b, q]}, -z], {i, 1, n}], {l, 1, n}], {Subscript[j, n], 0, Subscript[m, n] - 1}], {k, 1, n}, {Subscript[j, 1], 0, Subscript[m, 1] - 1}] /; Element[Subscript[m, n], Integers] && Subscript[m, n] > 0 && n <= q










Standard Form





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MathML Form







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</mo> <munderover> <mrow> <mtext> </mtext> <mo> &#8719; </mo> </mrow> <munder> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <mi> j </mi> <mo> &#8800; </mo> <mi> k </mi> </mrow> </munder> <mi> n </mi> </munderover> <mo> &#8290; </mo> <mfrac> <mn> 1 </mn> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> i </mi> </msub> <mo> + </mo> <msub> <mi> j </mi> <mi> i </mi> </msub> <mo> - </mo> <msub> <mi> j </mi> <mi> k </mi> </msub> </mrow> </mfrac> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mrow> <mi> p </mi> <mo> - </mo> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <msub> <mi> F </mi> <mrow> <mi> q </mi> <mo> - </mo> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <msub> <mi> j </mi> <mi> k </mi> </msub> <mo> - </mo> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> a </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mo> &#8230; 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Date Added to functions.wolfram.com (modification date)





2001-10-29