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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=-19/4, b>=a > For fixed z and a=-19/4, b=5/2





http://functions.wolfram.com/07.23.03.a9kn.01









  


  








Input Form





Hypergeometric2F1[-(19/4), 5/2, 3, z] == (16 Sqrt[2] (2 (1 - z)^(1/4) (-29260 - 109725 z + 1621881 z^2 - 4284734 z^3 + 4949958 z^4 - 2714985 z^5 + 580125 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-29260 - 109725 z + 1621881 z^2 - 4284734 z^3 + 4949958 z^4 - 2714985 z^5 + 580125 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (-29260 - 109725 z + 1621881 z^2 - 4284734 z^3 + 4949958 z^4 - 2714985 z^5 + 580125 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (-29260 - 109725 z + 1621881 z^2 - 4284734 z^3 + 4949958 z^4 - 2714985 z^5 + 580125 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (-29260 - 109725 z + 1621881 z^2 - 4284734 z^3 + 4949958 z^4 - 2714985 z^5 + 580125 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (-29260 - 95095 z - 23994 z^2 + 1871863 z^3 - 4886024 z^4 + 5400135 z^5 - 2831010 z^6 + 580125 z^7) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (13627845 Pi Sqrt[1 + Sqrt[1 - z]] z^2)








Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2007-05-02