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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=-31/8, b>=a > For fixed z and a=-31/8, b=27/8





http://functions.wolfram.com/07.23.03.bfg3.01









  


  








Input Form





Hypergeometric2F1[-(31/8), 27/8, 1, z] == -((2 2^(1/4) ((2 + Sqrt[2 - 2 Sqrt[1 - z]]) Sqrt[1 - z] (-3974983 + 33349784 z - 66459120 z^2 + 37128000 z^3) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-1240612 + 3974983 Sqrt[1 - z] - 104 (-313659 + 320671 Sqrt[1 - z]) z + 17680 (-7393 + 3759 Sqrt[1 - z]) z^2 - 1485120 (-117 + 25 Sqrt[1 - z]) z^3 - 74256000 z^4) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (5215595 Pi Sqrt[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