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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=39/8





http://functions.wolfram.com/07.23.03.bw12.01









  


  










Input Form





Hypergeometric2F1[-(3/8), 39/8, 2, z] == (1/(274505 Pi (-1 + z)^3 z)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-1 + z) (-805 + 18509 z - 35516 z^2 + 17680 z^3) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 10 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-1 + z) (-3381 + 10727 z - 10816 z^2 + 3536 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (-1 + z) (-805 + 18509 z - 35516 z^2 + 17680 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-34615 + 125779 z - 143676 z^2 + 53040 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