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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/07.23.06.0045.01









  


  










Input Form





Hypergeometric2F1[a, b, c, z] == ((Pi^2 Gamma[c] Csc[c Pi] (1 - x)^(c - a - b))/(Gamma[a] Gamma[b])) E^(I (c - a - b) Pi Floor[Arg[x - z]/(2 Pi)]) Sum[(1/((1 - x)^k k!)) (((Csc[(a + b - c) Pi]/(Gamma[1 - a - k] Gamma[1 - b - k])) E^(I (c - a - b) Pi Floor[Arg[x - z]/(2 Pi)]) - ((Sin[(c - a) Pi] Sin[(c - b) Pi] Gamma[a + k] Gamma[b + k])/Pi^2) (Csc[(a + b - c) Pi] E^(I (c - a - b) Pi Floor[Arg[x - z]/(2 Pi)]) + 2 I Floor[Arg[x - z]/(2 Pi)])) Hypergeometric2F1Regularized[-a + c, -b + c, c + k, x] + ((2 I x^(1 - c - k))/(Gamma[c - a] Gamma[c - b])) Floor[Arg[x - z]/(2 Pi)] (1 - x)^(k + a + b - c) Hypergeometric2F1Regularized[a - c + 1, b - c + 1, 2 - c - k, x]) (z - x)^k, {k, 0, Infinity}] /; !Element[c - a - b, Integers] && !Element[c, Integers] && Element[x, Reals] && x > 1










Standard Form





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MathML Form







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<apply> <times /> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <pi /> </apply> </apply> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <pi /> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> a </ci> <ci> k </ci> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> b </ci> <ci> k </ci> </apply> </apply> <apply> <power /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <pi /> <apply> <floor /> <apply> <times /> <apply> <arg /> <apply> 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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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