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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/07.24.06.0045.01









  


  










Input Form





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










Standard Form





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MathML Form







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</apply> </apply> <apply> <ci> Hypergeometric2F1Regularized </ci> <apply> <plus /> <ci> a </ci> <ci> k </ci> </apply> <apply> <plus /> <ci> b </ci> <ci> k </ci> </apply> <apply> <plus /> <ci> a </ci> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <ci> k </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <notin /> <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> <integers /> </apply> <apply> <in /> <ci> x </ci> <reals /> </apply> <apply> <gt /> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02