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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=7/4





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









  


  








Input Form





Hypergeometric2F1[-(1/4), 7/4, 1/2, z] == (1/(12 Pi^(3/2) (-1 + z))) (((-6 + 8 z) EllipticE[(1/2) (1 - Sqrt[z])] + (-6 + 8 z) EllipticE[(1/2) (1 + Sqrt[z])] + 3 EllipticK[(1/2) (1 - Sqrt[z])] - Sqrt[z] EllipticK[(1/2) (1 - Sqrt[z])] - 4 z EllipticK[(1/2) (1 - Sqrt[z])] + 3 EllipticK[(1/2) (1 + Sqrt[z])] + Sqrt[z] EllipticK[(1/2) (1 + Sqrt[z])] - 4 z EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[1/4]^2)








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