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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=13/4





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









  


  








Input Form





Hypergeometric2F1[1/4, 13/4, 6, -z] == (16384 Sqrt[2] (Sqrt[1 + z] (2048 + 3104 z + 483 z^2 - 259 z^3 + 224 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (2048 + 5152 z + 3587 z^2 + 224 z^3 - 35 z^4 + 224 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (2048 + 4640 z + 2667 z^2 - 49 z^3 + 56 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (2048 + 3104 z + 483 z^2 - 259 z^3 + 224 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (1382535 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