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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=-11/4, b>=a > For fixed z and a=-11/4, b=-3/4





http://functions.wolfram.com/07.23.03.ad3d.01









  


  








Input Form





Hypergeometric2F1[-(11/4), -(3/4), 3, -z] == (1/(21945 Pi z^2 Sqrt[1 + Sqrt[1 + z]])) (64 Sqrt[2] (-2 Sqrt[1 + z] (2 + 25 z - 194 z^2 + 25 z^3 + 2 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 (2 + 27 z - 169 z^2 - 169 z^3 + 27 z^4 + 2 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (4 + 53 z + 335 z^2 - 673 z^3 + z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 2 Sqrt[1 + z] (2 + 25 z - 194 z^2 + 25 z^3 + 2 z^4) EllipticK[(-1 + Sqrt[1 + z])/(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