Appell function F1: Integral representations (formula 07.36.07.0002)

AppellF1

$Mathematica Notation$

Hypergeometric Functions

AppellF1[a,b₁,b₂,c,z₁,z₂]

Integral representations

Contour integral representations

http://functions.wolfram.com/07.36.07.0002.01

Input Form

AppellF1[a, Subscript[b, 1], Subscript[b, 2], c, Subscript[z, 1], Subscript[z, 2]] == (1/(2 Pi I)^2) (Gamma[c]/(Gamma[a] Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]])) ContourIntegrate[(Gamma[a - s - t] Gamma[s] Gamma[Subscript[b, 1] - s] Gamma[t] Gamma[Subscript[b, 2] - t])/Gamma[c - s - t]/ ((-Subscript[z, 1])^s (-Subscript[z, 2])^t), {t, SuperStar[\[ScriptCapitalL]]}, {s, \[ScriptCapitalL]}] /; Abs[Arg[-Subscript[z, 1]]] < Pi && Abs[Arg[-Subscript[z, 2]]] < 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