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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=-1/2, b>=a > For fixed z and a=-1/2, b=1/4





http://functions.wolfram.com/07.23.03.ah5r.01









  


  








Input Form





Hypergeometric2F1[-(1/2), 1/4, 3, z] == (1/(315 Pi Sqrt[1 + Sqrt[1 - z]] z^2)) (8 Sqrt[2] (2 (1 + Sqrt[1 - z]) (1 - z)^(1/4) (-8 + 32 z + 21 z^2) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (-8 (1 + (1 - z)^(1/4) + Sqrt[1 - z] + (1 - z)^(3/4)) + 4 (9 + 8 (1 - z)^(1/4) + 8 Sqrt[1 - z] + 8 (1 - z)^(3/4)) z + (-73 + 21 (1 - z)^(1/4) + 21 Sqrt[1 - z] + 21 (1 - z)^(3/4)) z^2) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 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