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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=-9/4, b>=a > For fixed z and a=-9/4, b=-9/4





http://functions.wolfram.com/07.23.03.ae0t.01









  


  








Input Form





Hypergeometric2F1[-(9/4), -(9/4), -(1/2), z] == (1/(24 Pi^(3/2))) ((-4 (-3 + 30 z + 37 z^2) EllipticE[(1/2) (1 - Sqrt[z])] - 4 (-3 + 30 z + 37 z^2) EllipticE[(1/2) (1 + Sqrt[z])] + (-6 - 3 Sqrt[z] + 60 z + 86 z^(3/2) + 74 z^2 + 45 z^(5/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (-6 + 3 Sqrt[z] + 60 z - 86 z^(3/2) + 74 z^2 - 45 z^(5/2)) 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