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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=33/8





http://functions.wolfram.com/07.23.03.c7du.01









  


  








Input Form





Hypergeometric2F1[19/8, 33/8, 5, z] == -((65536 2^(1/4) (2 (2 + Sqrt[2 - 2 Sqrt[1 - z]]) Sqrt[1 - z] (1536 - 2128 z + 363 z^2 + 99 z^3) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (3072 (1 + Sqrt[1 - z]) - 32 (193 + 133 Sqrt[1 - z]) z + (3071 + 726 Sqrt[1 - z]) z^2 + 33 (1 + 6 Sqrt[1 - z]) z^3) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (2734875 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] (-1 + z)^2 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