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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=-21/8, b>=a > For fixed z and a=-21/8, b=-1/8





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









  


  








Input Form





Hypergeometric2F1[-(21/8), -(1/8), 1, z] == -((2 2^(1/4) (8 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-452 - 13 z + 3 z^2) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (443 + 1808 Sqrt[1 - z] + 1808 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] + (-626 + 52 Sqrt[1 - z] + 52 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z - 3 (-77 + 4 Sqrt[1 - z] + 4 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^2 - 48 z^3) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/(1365 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4)))








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