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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=15/8





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









  


  








Input Form





Hypergeometric2F1[5/8, 15/8, 2, z] == -((1/(21 Pi (-1 + z) z)) (16 2^(1/4) (1 + Sqrt[1 - z])^(1/4) (2 Sqrt[2] (-1 + z) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (Sqrt[2] - 2 Sqrt[1 + Sqrt[1 - z]] + 3 Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] - Sqrt[2] z + 2 Sqrt[1 + Sqrt[1 - z]] z) 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