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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=21/4, b>=a > For fixed z and a=21/4, b=21/4





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









  


  








Input Form





Hypergeometric2F1[21/4, 21/4, 4, -z] == -((256 Sqrt[2] ((160 + 1435 z + 7545 z^2 - 100463 z^3 + 26323 z^4) (1 + Sqrt[1 + z]) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (160 (1 + Sqrt[1 + z]) + 5 z (287 + 279 Sqrt[1 + z]) + 15 z^2 (503 + 481 Sqrt[1 + z]) + z^4 (26323 + 9945 Sqrt[1 + z]) - z^3 (100463 + 50603 Sqrt[1 + z])) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])]))/(6593535 Pi z^3 (1 + z)^(13/2) 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