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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=-15/4





http://functions.wolfram.com/07.23.03.ab0o.01









  


  








Input Form





Hypergeometric2F1[-(15/4), -(15/4), -(1/2), z] == (1/(90 Pi^(3/2))) ((2 Sqrt[z] (45 + 20985 z + 37767 z^2 + 6739 z^3) EllipticE[(1/2) (1 - Sqrt[z])] - 2 Sqrt[z] (45 + 20985 z + 37767 z^2 + 6739 z^3) EllipticE[(1/2) (1 + Sqrt[z])] - (-90 + 45 Sqrt[z] + 2565 z + 20985 z^(3/2) + 29325 z^2 + 37767 z^(5/2) + 30271 z^3 + 6739 z^(7/2) + 3465 z^4) EllipticK[(1/2) (1 - Sqrt[z])] + (90 + 45 Sqrt[z] - 2565 z + 20985 z^(3/2) - 29325 z^2 + 37767 z^(5/2) - 30271 z^3 + 6739 z^(7/2) - 3465 z^4) 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