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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.ahyh.01









  


  








Input Form





Hypergeometric2F1[1/4, 1/4, 1/2, -z] == (Gamma[3/4]^2/(Pi^(3/2) (z + 1)^(1/4))) (EllipticK[1/2 + (1/2) Sqrt[z/(z + 1)]] + EllipticK[1/2 - (1/2) Sqrt[z/(z + 1)]]) /; !IntervalMemberQ[Interval[{-Infinity, -1}], z]








Standard Form





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MathML Form







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Rule Form





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Contributed by





Brychkov Yu.A. (2006)


Date Added to functions.wolfram.com (modification date)





2007-05-02