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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=-13/8, b>=a > For fixed z and a=-13/8, b=41/8





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









  


  










Input Form





Hypergeometric2F1[-(13/8), 41/8, 1, z] == (2 2^(1/4) (Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-829849 + 7596465 z - 19303416 z^2 + 18983888 z^3 - 6460608 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 2 Sqrt[1 - z] (829849 - 7596465 z + 19303416 z^2 - 18983888 z^3 + 6460608 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 2 (-1 + z) (-141437 + 805203 z - 1203840 z^2 + 538384 z^3) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (829849 - 7596465 z + 19303416 z^2 - 18983888 z^3 + 6460608 z^4) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (546975 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] (-1 + z)^3)










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