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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=19/8





http://functions.wolfram.com/07.23.03.bxn2.01









  


  








Input Form





Hypergeometric2F1[1/8, 19/8, 1, z] == (2 2^(1/4) (-2 (2 + Sqrt[2 - 2 Sqrt[1 - z]]) Sqrt[1 - z] (-7 + 5 z) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (19 - 14 Sqrt[1 - z] + (-39 + 10 Sqrt[1 - z]) z + 20 z^2) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (33 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] (-1 + 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