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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.am80.01









  


  








Input Form





Hypergeometric2F1[13/4, 13/4, 3/2, z] == (1/(675 Pi^(3/2) Sqrt[z])) (2 ((2 (147 + 1338 z + 563 z^2) EllipticE[(1/2) (1 - Sqrt[z])])/ (-1 + z)^5 - (2 (147 + 1338 z + 563 z^2) EllipticE[(1/2) (1 + Sqrt[z])])/ (-1 + z)^5 - ((147 + 264 Sqrt[z] + 1074 z + 248 z^(3/2) + 315 z^2) EllipticK[(1/2) (1 - Sqrt[z])])/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^4) - ((147 - 264 Sqrt[z] + 1074 z - 248 z^(3/2) + 315 z^2) EllipticK[(1/2) (1 + Sqrt[z])])/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^5)) 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