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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] > Integral representations > Multiple integral representations





http://functions.wolfram.com/07.31.07.0006.01









  


  










Input Form





HypergeometricPFQ[{Subscript[a, 1], …, Subscript[a, p]}, {Subscript[b, 1], …, Subscript[b, p], Subscript[b, p + 1], …, Subscript[b, q]}, z] == Product[(Gamma[Subscript[b, k]]/(Gamma[Subscript[a, k]]* Gamma[Subscript[b, k] - Subscript[a, k]]))* Integrate[Product[Subscript[t, k]^(Subscript[a, k] - 1)*(1 - Subscript[t, k])^ (Subscript[b, k] - Subscript[a, k] - 1)*HypergeometricPFQ[{}, {Subscript[b, p + 1], …, Subscript[b, q]}, z*Product[Subscript[t, k], {k, 1, p}]], {k, 1, p}], {Subscript[t, 1], 0, 1}, {Subscript[t, 2], 0, 1}, …, {Subscript[t, p], 0, 1}], {k, 1, p}] /; Re[Subscript[b, k]] > Re[Subscript[a, k]] > 0 && 1 <= k <= p










Standard Form





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MathML Form







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





2001-10-29





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