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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=-13/4, b>=a > For fixed z and a=-13/4, b=3/4





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









  


  








Input Form





Hypergeometric2F1[-(13/4), 3/4, 1/2, z] == (1/(924 Pi^(3/2))) ((2 (231 - 951 z + 1072 z^2 - 384 z^3) EllipticE[(1/2) (1 - Sqrt[z])] + 2 (231 - 951 z + 1072 z^2 - 384 z^3) EllipticE[(1/2) (1 + Sqrt[z])] + (-231 + 177 Sqrt[z] + 951 z - 241 z^(3/2) - 1072 z^2 + 96 z^(5/2) + 384 z^3) EllipticK[(1/2) (1 - Sqrt[z])] + (-231 - 177 Sqrt[z] + 951 z + 241 z^(3/2) - 1072 z^2 - 96 z^(5/2) + 384 z^3) 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