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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 4 and fixed z > For fixed z and a=1/4, b>=a > For fixed z and a=1/4, b=1/4





http://functions.wolfram.com/07.23.03.ahz0.01









  


  








Input Form





Hypergeometric2F1[1/4, 1/4, 5, -z] == -((4096 Sqrt[2] (4 (32 + 132 z + 213 z^2 + 183 z^3) (1 + z + Sqrt[1 + z]) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (1155 z^4 + 128 (1 + Sqrt[1 + z]) + 48 z (13 + 11 Sqrt[1 + z]) + 6 z^3 (223 + 122 Sqrt[1 + z]) + 3 z^2 (413 + 284 Sqrt[1 + z])) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (1334025 Pi z^4 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