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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=-1/4, b>=a > For fixed z and a=-1/4, b=19/4





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









  


  








Input Form





Hypergeometric2F1[-(1/4), 19/4, 4, z] == (1/(225225 Pi z^3)) (256 (2 (-32 - 93 z - 288 z^2 + 2048 z^3) EllipticE[(1/2) (1 - Sqrt[1 - z])] - ((-32 - 69 z - 216 z^2 + 512 z^3) EllipticK[(1/2) (1 - Sqrt[1 - z])])/ Sqrt[1 - z] - (-32 - 93 z - 288 z^2 + 2048 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