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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=-11/2, b>=a > For fixed z and a=-11/2, b=5/4





http://functions.wolfram.com/07.23.03.a80e.01









  


  








Input Form





Hypergeometric2F1[-(11/2), 5/4, 2, z] == (-2 (1 - z)^(1/4) (221760 - 2351584 z + 6598816 z^2 - 9311232 z^3 + 7237780 z^4 - 2969890 z^5 + 504735 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (221760 - 2351584 z + 6598816 z^2 - 9311232 z^3 + 7237780 z^4 - 2969890 z^5 + 504735 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (221760 - 1021024 z + 2618688 z^2 - 3481664 z^3 + 2585620 z^4 - 1022010 z^5 + 168245 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (221760 - 2351584 z + 6598816 z^2 - 9311232 z^3 + 7237780 z^4 - 2969890 z^5 + 504735 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (221760 - 2351584 z + 6598816 z^2 - 9311232 z^3 + 7237780 z^4 - 2969890 z^5 + 504735 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (221760 - 2351584 z + 6598816 z^2 - 9311232 z^3 + 7237780 z^4 - 2969890 z^5 + 504735 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (360360 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] 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