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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=-3/2, b>=a > For fixed z and a=-3/2, b=1/4





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









  


  








Input Form





Hypergeometric2F1[-(3/2), 1/4, 5, z] == (64 Sqrt[2] (-2 (1 - z)^(1/4) (512 - 3328 z + 9696 z^2 - 18920 z^3 - 12320 z^4 + 1155 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (512 - 3328 z + 9696 z^2 - 18920 z^3 - 12320 z^4 + 1155 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (512 - 3584 z + 11312 z^2 - 23480 z^3 + 38060 z^4 + 385 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (512 - 3328 z + 9696 z^2 - 18920 z^3 - 12320 z^4 + 1155 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (512 - 3328 z + 9696 z^2 - 18920 z^3 - 12320 z^4 + 1155 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (512 - 3328 z + 9696 z^2 - 18920 z^3 - 12320 z^4 + 1155 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (1334025 Pi Sqrt[1 + Sqrt[1 - z]] z^4)








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