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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=-23/4, b>=a > For fixed z and a=-23/4, b=-5/2





http://functions.wolfram.com/07.23.03.9224.01









  


  








Input Form





Hypergeometric2F1[-(23/4), -(5/2), 2, z] == (2 (1 - z)^(1/4) (38456 + 4544472 z + 20271042 z^2 + 13955791 z^3 + 347520 z^4 - 32256 z^5 + 1920 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (38456 + 4544472 z + 20271042 z^2 + 13955791 z^3 + 347520 z^4 - 32256 z^5 + 1920 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (38456 + 4544472 z + 20271042 z^2 + 13955791 z^3 + 347520 z^4 - 32256 z^5 + 1920 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (38456 + 4544472 z + 20271042 z^2 + 13955791 z^3 + 347520 z^4 - 32256 z^5 + 1920 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (38456 + 4544472 z + 20271042 z^2 + 13955791 z^3 + 347520 z^4 - 32256 z^5 + 1920 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-38456 - 891152 z + 7670574 z^2 + 24203963 z^3 + 8504960 z^4 - 353664 z^5 + 32640 z^6 - 1920 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (908523 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z)








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