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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=-19/8





http://functions.wolfram.com/07.23.03.b4u8.01









  


  










Input Form





Hypergeometric2F1[-(47/8), -(19/8), 5, z] == (65536 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-8475870208 + 175079693984 z - 2064561404659 z^2 + 23700105772798 z^3 + 627775961632855 z^4 + 1148840633361988 z^5 + 394942970591211 z^6 + 2026427961294 z^7 - 142304013423 z^8 + 6270050160 z^9) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-8475870208 + 175079693984 z - 2064561404659 z^2 + 23700105772798 z^3 + 627775961632855 z^4 + 1148840633361988 z^5 + 394942970591211 z^6 + 2026427961294 z^7 - 142304013423 z^8 + 6270050160 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (-8475870208 + 175079693984 z - 2064561404659 z^2 + 23700105772798 z^3 + 627775961632855 z^4 + 1148840633361988 z^5 + 394942970591211 z^6 + 2026427961294 z^7 - 142304013423 z^8 + 6270050160 z^9) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (-4237935104 + 89129072656 z - 1064673591059 z^2 + 12228412752686 z^3 - 255679111849189 z^4 - 1077621152015296 z^5 - 791858669356461 z^6 - 85251625257546 z^7 + 4187897127909 z^8 - 290616824916 z^9 + 12540100320 z^10) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(37042556396008588425 Pi (1 + Sqrt[1 - z])^(1/4) 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