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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=-31/8, b>=a > For fixed z and a=-31/8, b=27/8





http://functions.wolfram.com/07.23.03.bfg7.01









  


  










Input Form





Hypergeometric2F1[-(31/8), 27/8, 3, z] == (256 2^(1/4) (-2 Sqrt[1 - z] (199640 + 1721895 z - 41953703 z^2 + 115452168 z^3 - 112497840 z^4 + 37128000 z^5) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (199640 + 1721895 z - 41953703 z^2 + 115452168 z^3 - 112497840 z^4 + 37128000 z^5) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (199640 + 1721895 z - 41953703 z^2 + 115452168 z^3 - 112497840 z^4 + 37128000 z^5) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 8 (24955 + 199640 z + 3954824 z^2 - 23451389 z^3 + 43194450 z^4 - 33229560 z^5 + 9282000 z^6) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (9560185635 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^2)










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