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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=-15/4, b>=a > For fixed z and a=-15/4, b=1/4





http://functions.wolfram.com/07.23.03.abb0.01









  


  








Input Form





Hypergeometric2F1[-(15/4), 1/4, -(1/2), z] == (1/(30 Pi^(3/2))) ((2 Sqrt[z] (15 - 255 z + 336 z^2 - 128 z^3) EllipticE[(1/2) (1 - Sqrt[z])] + 2 Sqrt[z] (-15 + 255 z - 336 z^2 + 128 z^3) EllipticE[(1/2) (1 + Sqrt[z])] + (30 - 15 Sqrt[z] + 45 z + 255 z^(3/2) - 75 z^2 - 336 z^(5/2) + 32 z^3 + 128 z^(7/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (30 + 15 Sqrt[z] + 45 z - 255 z^(3/2) - 75 z^2 + 336 z^(5/2) + 32 z^3 - 128 z^(7/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^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