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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=19/4





http://functions.wolfram.com/07.23.03.aem5.01









  


  








Input Form





Hypergeometric2F1[-(9/4), 19/4, 4, z] == (1/(5360355 Pi z^3)) (256 (2 (-96 - 447 z - 2607 z^2 + 62080 z^3 - 124928 z^4 + 65536 z^5) EllipticE[(1/2) (1 - Sqrt[1 - z])] + Sqrt[1 - z] (96 + 471 z + 2736 z^2 - 19456 z^3 + 16384 z^4) EllipticK[(1/2) (1 - Sqrt[1 - z])] - (-96 - 447 z - 2607 z^2 + 62080 z^3 - 124928 z^4 + 65536 z^5) 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