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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Series representations > Generalized power series > Expansions on branch cuts > For the function itself





http://functions.wolfram.com/07.23.06.0046.01









  


  










Input Form





Hypergeometric2F1[a, b, c, z] \[Proportional] (Gamma[c]/(Gamma[a] Gamma[b] Gamma[-a + c] Gamma[-b + c])) E^(I (c - a - b) Pi Floor[Arg[x - z]/(2 Pi)]) (-2 I Pi Floor[Arg[x - z]/(2 Pi)] Gamma[a] Gamma[b] Hypergeometric2F1Regularized[a, b, 1 + a + b - c, 1 - x] + E^(I (c - a - b) Pi Floor[Arg[x - z]/(2 Pi)]) MeijerG[{{1 - a, 1 - b}, {}}, {{0, -a - b + c}, {}}, 1 - x]) + O[z - x] /; 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