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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=13/4





http://functions.wolfram.com/07.23.03.am8g.01









  


  








Input Form





Hypergeometric2F1[13/4, 13/4, 11/2, z] == (1/(75 Pi^(3/2) z^(9/2))) (224 ((2 (336 - 444 z + 113 z^2) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z) - (2 (336 - 444 z + 113 z^2) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z) - ((336 - 168 Sqrt[z] - 276 z + 68 z^(3/2) + 45 z^2) EllipticK[(1/2) (1 - Sqrt[z])])/(-1 + Sqrt[z]) - ((336 + 168 Sqrt[z] - 276 z - 68 z^(3/2) + 45 z^2) EllipticK[(1/2) (1 + Sqrt[z])])/(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