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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Series representations > Residue representations > General case





http://functions.wolfram.com/07.23.06.0035.01









  


  








Input Form





Hypergeometric2F1[a, b, c, z] == (-(Gamma[c]/(Gamma[a] Gamma[b]))) (Sum[Residue[((Gamma[s] Gamma[b - s])/((-z)^s Gamma[c - s])) Gamma[a - s], {s, a + j}], {j, 0, Infinity}] + Sum[Residue[((Gamma[s] Gamma[a - s])/((-z)^s Gamma[c - s])) Gamma[b - s], {s, b + j}], {j, 0, Infinity}]) /; Abs[z] > 1 && !Element[a - b, Integers]








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