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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=1/8, b>=a > For fixed z and a=1/8, b=27/8





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









  


  








Input Form





Hypergeometric2F1[1/8, 27/8, 4, z] == -((2048 2^(1/4) ((2 + Sqrt[2 - 2 Sqrt[1 - z]]) Sqrt[1 - z] (128 + 139 z + 180 z^2) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (128 (1 + Sqrt[1 - z]) + (59 + 139 Sqrt[1 - z]) z + 20 (4 + 9 Sqrt[1 - z]) z^2 + 360 z^3) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (504735 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^3))








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