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variants of this functions
Hypergeometric2F1Regularized






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Series representations > Generalized power series > Expansions on branch cuts > For the function itself





http://functions.wolfram.com/07.24.06.0044.01









  


  










Input Form





Hypergeometric2F1Regularized[a, b, c, z] == (1/(Gamma[a] Gamma[b] Gamma[c - a] Gamma[c - b])) E^(I (c - a - b) Pi Floor[Arg[x - z]/(2 Pi)]) Sum[(1/k!) (-2 Pi I Floor[Arg[x - z]/(2 Pi)] (-1)^k Gamma[a + k] Gamma[b + k] Hypergeometric2F1Regularized[a + k, b + k, 1 + a + b - c + k, 1 - x] + E^(I (c - a - b) Pi Floor[Arg[x - z]/(2 Pi)]) MeijerG[{{1 - a - k, 1 - b - k}, {}}, {{0, c - a - b - k}, {}}, 1 - x]) (z - x)^k, {k, 0, Infinity}] /; Element[x, Reals] && x > 1










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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