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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=5/4, b>=a > For fixed z and a=5/4, b=5/4





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









  


  








Input Form





Hypergeometric2F1[5/4, 5/4, 11/2, z] == (1/(2535 Pi^(3/2) z^(9/2))) (224 (2 (-1680 + 4860 z - 4609 z^2 + 1397 z^3) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (-1680 + 4860 z - 4609 z^2 + 1397 z^3) EllipticE[(1/2) (1 + Sqrt[z])] - (-1680 - 840 Sqrt[z] + 4860 z + 2360 z^(3/2) - 4609 z^2 - 2137 z^(5/2) + 1397 z^3 + 585 z^(7/2)) EllipticK[(1/2) (1 - Sqrt[z])] - (1680 - 840 Sqrt[z] - 4860 z + 2360 z^(3/2) + 4609 z^2 - 2137 z^(5/2) - 1397 z^3 + 585 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