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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=-9/2, b>=a > For fixed z and a=-9/2, b=11/4





http://functions.wolfram.com/07.23.03.aa3o.01









  


  








Input Form





Hypergeometric2F1[-(9/2), 11/4, 3, z] == (2 (-1920 - 9600 z + 177968 z^2 - 518672 z^3 + 641784 z^4 - 371280 z^5 + 82875 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-1920 - 9600 z + 177968 z^2 - 518672 z^3 + 641784 z^4 - 371280 z^5 + 82875 z^6) EllipticE[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1920 + 9600 z - 177968 z^2 + 518672 z^3 - 641784 z^4 + 371280 z^5 - 82875 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (1920 + 9600 z - 177968 z^2 + 518672 z^3 - 641784 z^4 + 371280 z^5 - 82875 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (1920 + 9600 z - 177968 z^2 + 518672 z^3 - 641784 z^4 + 371280 z^5 - 82875 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (1920 + 10560 z + 7792 z^2 - 196352 z^3 + 397800 z^4 - 304980 z^5 + 82875 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (45045 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^2)








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