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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 8 and fixed z and a<0 > For fixed z and a=-19/8, b>=a > For fixed z and a=-19/8, b=15/8





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









  


  








Input Form





Hypergeometric2F1[-(19/8), 15/8, 2, z] == (1/(39501 Pi z)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-209 + 2433 z - 3672 z^2 + 1560 z^3) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 12 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (418 - 801 z + 390 z^2) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (-209 + 2433 z - 3672 z^2 + 1560 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-4807 + 12195 z - 10620 z^2 + 3120 z^3) EllipticK[1/2 - 1/(Sqrt[2] 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