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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/07.23.06.0068.01









  


  










Input Form





Hypergeometric2F1[a, b, c, z] == ((Csc[(a - b) Pi] Gamma[c])/(Gamma[a] Gamma[b])) ((Sin[(a - c) Pi] Sum[Residue[((Gamma[a - s] Gamma[1 + a - c - s])/ ((-(1/z))^s Gamma[1 + a - b - s])) Gamma[s], {s, -j}], {j, 0, Infinity}])/(-z)^a + (Sin[(b - c) Pi] Sum[Residue[((Gamma[b - s] Gamma[1 + b - c - s])/ ((-(1/z))^s Gamma[1 + b - a - s])) Gamma[s], {s, -j}], {j, 0, Infinity}])/(-z)^b) /; 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)





2007-05-02