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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 8 and fixed z and a<0 > For fixed z and a=-19/8, b>=a > For fixed z and a=-19/8, b=31/8





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









  


  








Input Form





Hypergeometric2F1[-(19/8), 31/8, 1, z] == (1/(168245 Pi)) (2^(3/4) (1 + Sqrt[1 - z])^(1/4) (104 (4723 - 27472 z + 28560 z^2) EllipticE[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 52 (4723 - 27472 z + 28560 z^2) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (1/z) (5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-33649 + 312728 z - 597584 z^2 + 297024 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]) - (1/(Sqrt[1 - z] z)) (Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-168245 + 1686438 z - 3702192 z^2 + 2227680 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - 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