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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=3/4, b>=a > For fixed z and a=3/4, b=21/4





http://functions.wolfram.com/07.23.03.aj9i.01









  


  










Input Form





Hypergeometric2F1[3/4, 21/4, 6, -z] == (1/(6593535 Pi z^5 (1 + z)^(1/4))) (16384 (2 Sqrt[1 + z] (6144 - 2784 z + 2041 z^2 - 1740 z^3 + 1680 z^4) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - (6144 (1 + Sqrt[1 + z]) + 840 z^4 (1 + 2 Sqrt[1 + z]) - 96 z (13 + 29 Sqrt[1 + z]) - 20 z^3 (40 + 87 Sqrt[1 + z]) + z^2 (913 + 2041 Sqrt[1 + z])) EllipticK[1/2 - 1/(2 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