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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=1/2





http://functions.wolfram.com/07.23.03.agj6.01









  


  








Input Form





Hypergeometric2F1[-(3/4), 1/2, 6, z] == (512 Sqrt[2] (2 (1 - z)^(1/4) (2048 - 12480 z + 32244 z^2 - 46466 z^3 + 44499 z^4 + 3360 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (2048 - 12480 z + 32244 z^2 - 46466 z^3 + 44499 z^4 + 3360 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (2048 - 12480 z + 32244 z^2 - 46466 z^3 + 44499 z^4 + 3360 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (2048 - 12480 z + 32244 z^2 - 46466 z^3 + 44499 z^4 + 3360 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (2048 - 12480 z + 32244 z^2 - 46466 z^3 + 44499 z^4 + 3360 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (2048 - 13504 z + 38292 z^2 - 61514 z^3 + 65233 z^4 - 57120 z^5 + 3360 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/(10599435 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








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