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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=3/4, b>=a > For fixed z and a=3/4, b=15/4





http://functions.wolfram.com/07.23.03.aj3d.01









  


  








Input Form





Hypergeometric2F1[3/4, 15/4, 3/2, z] == (1/(462 Pi^(3/2))) ((-((2 (93 - 93 z + 32 z^2) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^3) - (2 (93 - 93 z + 32 z^2) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^3 + ((45 + 48 Sqrt[z] - 69 z - 24 z^(3/2) + 32 z^2) EllipticK[(1/2) (1 - Sqrt[z])])/((-1 + Sqrt[z])^3 (1 + Sqrt[z])^2 Sqrt[z]) + ((45 - 48 Sqrt[z] - 69 z + 24 z^(3/2) + 32 z^2) EllipticK[(1/2) (1 + Sqrt[z])])/((-1 + Sqrt[z])^2 (1 + Sqrt[z])^3 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