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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=1/4





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









  


  








Input Form





Hypergeometric2F1[-(1/4), 1/4, 5, -z] == (1/(3828825 Pi z^4)) (4096 (1 + z)^(1/4) (2 (-128 - 656 z - 1405 z^2 - 1770 z^3 + 1155 z^4) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + (-1155 z^4 + 128 (1 + Sqrt[1 + z]) + 16 z (41 + 35 Sqrt[1 + z]) + 30 z^3 (59 + 36 Sqrt[1 + z]) + 5 z^2 (281 + 200 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