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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 4 and fixed z > For fixed z and a=-23/4, b>=a > For fixed z and a=-23/4, b=3/2





http://functions.wolfram.com/07.23.03.9620.01









  


  








Input Form





Hypergeometric2F1[-(23/4), 3/2, 1, z] == (1/(168245 Pi Sqrt[1 + Sqrt[1 - z]])) (Sqrt[2] (-2 (1 - z)^(1/4) (-413841 + 2362657 z - 5107790 z^2 + 5391074 z^3 - 2807805 z^4 + 580125 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (-413841 + 2362657 z - 5107790 z^2 + 5391074 z^3 - 2807805 z^4 + 580125 z^5) EllipticE[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-413841 + 2362657 z - 5107790 z^2 + 5391074 z^3 - 2807805 z^4 + 580125 z^5) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-413841 + 2362657 z - 5107790 z^2 + 5391074 z^3 - 2807805 z^4 + 580125 z^5) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-413841 + 2362657 z - 5107790 z^2 + 5391074 z^3 - 2807805 z^4 + 580125 z^5) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-77351 - 374710 z + 2713983 z^2 - 5782452 z^3 + 5859815 z^4 - 2923830 z^5 + 580125 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))








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