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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=-3/8, b>=a > For fixed z and a=-3/8, b=25/8





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









  


  








Input Form





Hypergeometric2F1[-(3/8), 25/8, 2, z] == (16 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (9 - 296 z + 320 z^2) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (9 (1 + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + Sqrt[1 - z]) - (89 + 296 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + 296 Sqrt[1 - z]) z + 80 (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]])]))/ (1683 Pi (1 + Sqrt[1 - z])^(1/4) (-1 + z) 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