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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=17/8, b>=a > For fixed z and a=17/8, b=37/8





http://functions.wolfram.com/07.23.03.c6l1.01









  


  








Input Form





Hypergeometric2F1[17/8, 37/8, 3, z] == (256 2^(1/4) (-8 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (130 - 520 z - 99 z^2 + 27 z^3) EllipticE[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 4 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (130 - 520 z - 99 z^2 + 27 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 4 Sqrt[1 - z] (130 - 520 z - 99 z^2 + 27 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-1 + z) (-520 + 1755 z - 1359 z^2 + 432 z^3) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(356265 Pi (1 + Sqrt[1 - z])^(1/4) (-1 + z)^4 z^2)








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