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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=13/8





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









  


  








Input Form





Hypergeometric2F1[-(1/8), 13/8, 1, z] == (1/(5 Pi (-1 + z) z)) (2 2^(1/4) (1 + Sqrt[1 - z])^(1/4) (12 Sqrt[2] (-1 + z) z EllipticE[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-5 (-1 + Sqrt[1 - z]) Sqrt[1 + Sqrt[1 - z]] + (6 Sqrt[2] - 5 Sqrt[1 + Sqrt[1 - z]] + 6 Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z]) z - 6 Sqrt[2] z^2) 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