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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=17/4





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









  


  








Input Form





Hypergeometric2F1[1/4, 17/4, 6, -z] == (16384 Sqrt[2] (Sqrt[1 + z] (-2048 - 672 z + 429 z^2 - 368 z^3 + 384 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (-2048 - 2720 z - 243 z^2 + 61 z^3 + 16 z^4 + 384 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-2048 - 2208 z + 69 z^2 - 65 z^3 + 96 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-2048 - 672 z + 429 z^2 - 368 z^3 + 384 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (2567565 Pi z^5 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