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variants of this functions
HypergeometricPFQRegularized






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.32.07.0005.01









  


  










Input Form





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










Standard Form





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MathML Form







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





2001-10-29