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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=-47/8, b>=a > For fixed z and a=-47/8, b=-21/8





http://functions.wolfram.com/07.23.03.b4sz.01









  


  










Input Form





Hypergeometric2F1[-(47/8), -(21/8), 4, z] == (2048 2^(1/4) (2 Sqrt[1 - z] (55762304 - 1361384375 z + 24609473070 z^2 + 733535393335 z^3 + 1633005019520 z^4 + 682870787655 z^5 + 12885946710 z^6 - 849703335 z^7 + 37662300 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (55762304 - 1361384375 z + 24609473070 z^2 + 733535393335 z^3 + 1633005019520 z^4 + 682870787655 z^5 + 12885946710 z^6 - 849703335 z^7 + 37662300 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (55762304 - 1361384375 z + 24609473070 z^2 + 733535393335 z^3 + 1633005019520 z^4 + 682870787655 z^5 + 12885946710 z^6 - 849703335 z^7 + 37662300 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (55762304 - 1396235815 z + 25454620490 z^2 - 966256464065 z^3 - 5243672648180 z^4 - 5227879602785 z^5 - 950493089910 z^6 + 26697339825 z^7 - 1740835200 z^8 + 75324600 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (1724977000021275 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] 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