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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=3/4





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









  


  










Input Form





Hypergeometric2F1[3/4, 3/4, 11/2, z] == (1/(4235 Pi^(3/2) z^(9/2))) (8 (8 Sqrt[z] (-70 + 255 z - 336 z^2 + 183 z^3) EllipticE[(1/2) (1 - Sqrt[z])] + 8 Sqrt[z] (-70 + 255 z - 336 z^2 + 183 z^3) EllipticE[(1/2) (1 + Sqrt[z])] - (560 - 280 Sqrt[z] - 2460 z + 1020 z^(3/2) + 4155 z^2 - 1344 z^(5/2) - 3282 z^3 + 732 z^(7/2) + 1155 z^4) EllipticK[(1/2) (1 - Sqrt[z])] + (560 + 280 Sqrt[z] - 2460 z - 1020 z^(3/2) + 4155 z^2 + 1344 z^(5/2) - 3282 z^3 - 732 z^(7/2) + 1155 z^4) 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