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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=5/4, b>=a > For fixed z and a=5/4, b=19/4





http://functions.wolfram.com/07.23.03.ak20.01









  


  








Input Form





Hypergeometric2F1[5/4, 19/4, 6, -z] == (1/(266805 Pi z^5 (1 + z)^(1/4))) (16384 (2 Sqrt[1 + z] (2048 + 96 z - 45 z^2 + 20 z^3) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - (-40 z^4 + 2048 (1 + Sqrt[1 + z]) + 20 z^3 (4 + Sqrt[1 + z]) - 15 z^2 (11 + 3 Sqrt[1 + z]) + 32 z (19 + 3 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