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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=7/8, b>=a > For fixed z and a=7/8, b=45/8





http://functions.wolfram.com/07.23.03.c1h0.01









  


  








Input Form





Hypergeometric2F1[7/8, 45/8, 5, z] == (32768 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-1 + z) (-3072 - 2272 z - 2207 z^2 - 2772 z^3 + 11088 z^4) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-1 + z) (-384 - 347 z - 352 z^2 + 1848 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-384 - 179 z - 149 z^2 - 4004 z^3 + 3696 z^4) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-1 + z) (-3072 - 2272 z - 2207 z^2 - 2772 z^3 + 11088 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (373484475 Pi (-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