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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=-7/2





http://functions.wolfram.com/07.23.03.9136.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(7/2), 1, z] == (2 (1 - z)^(1/4) (2532512 + 31727096 z + 61137440 z^2 + 21759787 z^3 + 232960 z^4 - 8960 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (2532512 + 31727096 z + 61137440 z^2 + 21759787 z^3 + 232960 z^4 - 8960 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-2532512 - 31727096 z - 61137440 z^2 - 21759787 z^3 - 232960 z^4 + 8960 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-2532512 - 31727096 z - 61137440 z^2 - 21759787 z^3 - 232960 z^4 + 8960 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-2532512 - 31727096 z - 61137440 z^2 - 21759787 z^3 - 232960 z^4 + 8960 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-917360 + 1842200 z + 47330036 z^2 + 58716231 z^3 + 10635520 z^4 - 234752 z^5 + 8960 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (403788 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - 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