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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=23/8





http://functions.wolfram.com/07.23.03.c01r.01









  


  








Input Form





Hypergeometric2F1[5/8, 23/8, 1, z] == (1/(105 Pi (-1 + z)^3)) (2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-8 (-1 + z) (-11 + 5 z) EllipticE[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 4 (-1 + z) (-11 + 5 z) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-1 + z) (21 - 13 z + 4 z^2) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])])/z - (3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (35 - 29 z + 10 z^2) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])])/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