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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] > Integral representations > Multiple integral representations





http://functions.wolfram.com/07.28.07.0005.01









  


  










Input Form





HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, 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))/ (1 - z Product[Subscript[t, k], {k, 1, 3}])^Subscript[a, 4], {k, 1, 3}], {Subscript[t, 3], 0, 1}, {Subscript[t, 2], 0, 1}, {Subscript[t, 1], 0, 1}], {k, 1, 3}] /; Re[Subscript[b, k]] > Re[Subscript[a, k]] > 0 && 1 <= k <= 3 && Abs[Arg[1 - z]] < Pi










Standard Form





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MathML Form







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Rule Form





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





2001-10-29





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