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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=-7/8





http://functions.wolfram.com/07.23.03.bmd6.01









  


  








Input Form





Hypergeometric2F1[-(19/8), -(7/8), 1, z] == (1/(4389 Pi (1 + Sqrt[1 - z])^(1/4))) (2 2^(1/4) (-8 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-680 - 539 z + 49 z^2) EllipticE[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (1669 - 2720 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) - 2720 Sqrt[1 - z] + (7642 - 2156 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) - 2156 Sqrt[1 - z]) z + 49 (1 + 4 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + 4 Sqrt[1 - z]) z^2) EllipticK[1/2 - (1 - z)^(1/4)/(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