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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=-3/2, b>=a > For fixed z and a=-3/2, b=3/4





http://functions.wolfram.com/07.23.03.afl1.01









  


  








Input Form





Hypergeometric2F1[-(3/2), 3/4, 2, z] == -((1/(15 Pi Sqrt[1 + Sqrt[1 - z]] z)) (Sqrt[2] (2 (1 + Sqrt[1 - z]) (-12 - 14 z + 5 z^2) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (12 (1 + (1 - z)^(1/4) + Sqrt[1 - z] + (1 - z)^(3/4)) - 2 (-7 - 7 (1 - z)^(1/4) - 7 Sqrt[1 - z] + 5 (1 - z)^(3/4)) z + 5 (-1 - (1 - z)^(1/4) - Sqrt[1 - z] + (1 - z)^(3/4)) z^2) EllipticK[1/2 - (1 - z)^(1/4)/(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