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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Series representations > Residue representations > Logarithmic cases





http://functions.wolfram.com/07.23.06.0071.01









  


  










Input Form





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





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