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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=15/4





http://functions.wolfram.com/07.23.03.ahq5.01









  


  








Input Form





Hypergeometric2F1[-(1/4), 15/4, 4, -z] == (1/(45045 Pi z^3 Sqrt[1 + Sqrt[1 + z]])) (256 Sqrt[2] ((32 - 41 z + 80 z^2 + 384 z^3) (1 + Sqrt[1 + z]) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (384 z^3 + 32 (1 + Sqrt[1 + z]) + 16 z^2 (5 + 6 Sqrt[1 + z]) - z (41 + 49 Sqrt[1 + z])) 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