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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=-5/4, b>=a > For fixed z and a=-5/4, b=-1/4





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









  


  








Input Form





Hypergeometric2F1[-(5/4), -(1/4), 6, -z] == (16384 Sqrt[2] ((-(2048 + 16672 z + 61475 z^2 + 140300 z^3 + 255250 z^4 - 977428 z^5 + 13923 z^6)) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - Sqrt[1 + z] (2048 + 16672 z + 61475 z^2 + 140300 z^3 + 255250 z^4 - 977428 z^5 + 13923 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-2048 - 16160 z - 57675 z^2 - 127625 z^3 - 229025 z^4 + 431613 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (2048 + 16672 z + 61475 z^2 + 140300 z^3 + 255250 z^4 - 977428 z^5 + 13923 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (4846248225 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