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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=5/8, b>=a > For fixed z and a=5/8, b=23/8





http://functions.wolfram.com/07.23.03.c01t.01









  


  








Input Form





Hypergeometric2F1[5/8, 23/8, 2, z] == -((1/(315 Pi (-1 + z)^2 z)) (16 2^(1/4) (1 + Sqrt[1 - z])^(1/4) (2 Sqrt[2] (7 - 17 z + 10 z^2) EllipticE[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-7 (Sqrt[2] - 5 Sqrt[1 + Sqrt[1 - z]] + 6 Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z]) + (17 Sqrt[2] - 55 Sqrt[1 + Sqrt[1 - z]] + 30 Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z]) z - 10 (Sqrt[2] - 2 Sqrt[1 + Sqrt[1 - z]]) z^2) 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