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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,r] > Representations through more general functions > Through hypergeometric functions > Involving pFq





http://functions.wolfram.com/07.35.26.0002.01









  


  










Input Form





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]}}, z, r] == Sum[(Product[If[j == k, 1, Gamma[Subscript[b, j] - Subscript[b, k]]] Product[Gamma[1 + Subscript[b, k] - Subscript[a, j]], {j, 1, n}], {j, 1, m}]/Product[Gamma[Subscript[a, j] - Subscript[b, k]] Product[Gamma[1 - Subscript[b, j] + Subscript[b, k]], {j, m + 1, q}], {j, n + 1, p}]) z^(Subscript[b, k]/r) HypergeometricPFQ[ {1 + Subscript[b, k] - Subscript[a, 1], \[Ellipsis], 1 + Subscript[b, k] - Subscript[a, p]}, {1 + Subscript[b, k] - Subscript[b, 1], \[Ellipsis], 1 + Subscript[b, k] - Subscript[b, k - 1], 1 + Subscript[b, k] - Subscript[b, k + 1], \[Ellipsis], 1 + Subscript[b, k] - Subscript[b, q]}, (-1)^(p - m - n) z^(1/r)], {k, 1, m}] /; (p < q || (p == q && Abs[z] < 1)) && ForAll[{j, k}, Element[{j, k}, Integers] && j != k && 1 <= j <= m && 1 <= k <= m, !Element[Subscript[b, j] - Subscript[b, k], Integers]]










Standard Form





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MathML Form







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





2001-10-29