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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=21/8





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









  


  










Input Form





Hypergeometric2F1[1/8, 21/8, 1, z] == (2 2^(1/4) (12 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (3 - 2 z) (1 - z)^(1/4) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (47 - 18 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) - 18 Sqrt[1 - z] + (-95 + 12 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + 12 Sqrt[1 - z]) z + 48 z^2) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(65 Pi (1 + Sqrt[1 - z])^(1/4) (-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