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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=37/8





http://functions.wolfram.com/07.23.03.by0n.01









  


  








Input Form





Hypergeometric2F1[1/8, 37/8, 4, z] == (2048 2^(1/4) ((2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-128 - 213 z - 520 z^2 + 1344 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])])/(1 - z)^(3/4) - (Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-128 - 213 z - 520 z^2 + 1344 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])])/ (1 - z)^(3/4) - ((-128 - 213 z - 520 z^2 + 1344 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])])/ Sqrt[1 - z] + (128 + 293 z + 720 z^2 + 5376 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (6373185 Pi (1 + Sqrt[1 - z])^(1/4) z^3)








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