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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=19/4





http://functions.wolfram.com/07.23.03.aga5.01









  


  








Input Form





Hypergeometric2F1[-(5/4), 19/4, 1, z] == (1/(1155 Pi (-1 + z)^3)) (2 (-4 (-1 + z) (-1059 + 6174 z - 9216 z^2 + 4096 z^3) EllipticE[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (-963 + 4119 z - 5184 z^2 + 2048 z^3) EllipticK[(1/2) (1 - Sqrt[1 - z])] + 2 (-1 + z) (-1059 + 6174 z - 9216 z^2 + 4096 z^3) EllipticK[(1/2) (1 - Sqrt[1 - z])]))








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