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variants of this functions
Hypergeometric2F1Regularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Series representations > Residue representations





http://functions.wolfram.com/07.24.06.0069.01









  


  








Input Form





Hypergeometric2F1Regularized[a, a + n, c, z] == (-(1/(Gamma[a] Gamma[b]))) (Sum[Residue[((Gamma[s] Gamma[a + n - s])/((-z)^s Gamma[c - s])) Gamma[a - s], {s, a + j}], {j, 0, n - 1}] + Sum[Residue[(Gamma[s]/((-z)^s Gamma[c - s])) Gamma[a - s] Gamma[a + n - s], {s, a + n + j}], {j, 0, Infinity}]) /; Abs[z] > 1 && Element[n, Integers] && n >= 0








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)





2007-05-02