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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=29/8





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









  


  








Input Form





Hypergeometric2F1[1/8, 29/8, 1, z] == -((2 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (443 - 599 z + 240 z^2) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (-922 + 443 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + 443 Sqrt[1 - z] + (2818 - 599 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) - 599 Sqrt[1 - z]) z + 24 (-119 + 10 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + 10 Sqrt[1 - z]) z^2 + 960 z^3) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (1365 Pi (1 + Sqrt[1 - z])^(1/4) (-1 + z)^3))








Standard Form





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MathML Form







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</semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02