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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=-13/8





http://functions.wolfram.com/07.23.03.b4vx.01









  


  










Input Form





Hypergeometric2F1[-(47/8), -(13/8), 6, z] == (524288 2^(1/4) (-2 Sqrt[1 - z] (-14275149824 + 249313261184 z - 2245702635345 z^2 + 15084805408790 z^3 - 108218114659655 z^4 - 1143742748275260 z^5 - 892298809125255 z^6 - 31292734233930 z^7 + 3438185717655 z^8 - 329489886960 z^9 + 17299549800 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-14275149824 + 249313261184 z - 2245702635345 z^2 + 15084805408790 z^3 - 108218114659655 z^4 - 1143742748275260 z^5 - 892298809125255 z^6 - 31292734233930 z^7 + 3438185717655 z^8 - 329489886960 z^9 + 17299549800 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (-14275149824 + 249313261184 z - 2245702635345 z^2 + 15084805408790 z^3 - 108218114659655 z^4 - 1143742748275260 z^5 - 892298809125255 z^6 - 31292734233930 z^7 + 3438185717655 z^8 - 329489886960 z^9 + 17299549800 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-14275149824 + 258235229824 z - 2400059663105 z^2 + 16463491345535 z^3 - 117427411640305 z^4 + 2278228923858755 z^5 + 5015207817218025 z^6 + 1506789933691965 z^7 - 66288736517835 z^8 + 7234571921265 z^9 - 678009278700 z^10 + 34599099600 z^11) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (879697905549049752165 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^5)










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