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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=-1/2





http://functions.wolfram.com/07.23.03.9403.01









  


  








Input Form





Hypergeometric2F1[-(23/4), -(1/2), 1, z] == (1/(168245 Pi Sqrt[1 + Sqrt[1 - z]])) (Sqrt[2] (2 (1 - z)^(1/4) (413841 + 293452 z - 204428 z^2 + 105236 z^3 - 32396 z^4 + 4420 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (413841 + 293452 z - 204428 z^2 + 105236 z^3 - 32396 z^4 + 4420 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (413841 + 293452 z - 204428 z^2 + 105236 z^3 - 32396 z^4 + 4420 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (413841 + 293452 z - 204428 z^2 + 105236 z^3 - 32396 z^4 + 4420 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (413841 + 293452 z - 204428 z^2 + 105236 z^3 - 32396 z^4 + 4420 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-77351 + 838816 z - 319832 z^2 + 220640 z^3 - 111008 z^4 + 33280 z^5 - 4420 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 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