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variants of this functions
HypergeometricPFQRegularized






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] > Integral representations > On the real axis > Of the direct function





http://functions.wolfram.com/07.32.07.0001.01









  


  










Input Form





HypergeometricPFQRegularized[{Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z] == (1/(Gamma[Subscript[a, p]] Gamma[Subscript[b, q] - Subscript[a, p]])) Integrate[t^(Subscript[a, p] - 1) (1 - t)^(Subscript[b, q] - Subscript[a, p] - 1) HypergeometricPFQRegularized[ {Subscript[a, 1], \[Ellipsis], Subscript[a, p - 1]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q - 1]}, z t], {t, 0, 1}] /; (Re[Subscript[b, q]] > Re[Subscript[a, p]] > 0 && p <= q) || (Re[Subscript[b, q]] > Re[Subscript[a, p]] > 0 && p == q + 1 && 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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