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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=-41/8, b>=a > For fixed z and a=-41/8, b=27/8





http://functions.wolfram.com/07.23.03.b9bb.01









  


  










Input Form





Hypergeometric2F1[-(41/8), 27/8, 5, z] == (65536 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-32117760 + 58548000 z + 50131725 z^2 + 156981825 z^3 - 6530142905 z^4 + 20364038123 z^5 - 28534353120 z^6 + 21327371520 z^7 - 8325058560 z^8 + 1341849600 z^9) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + 2 (-16058880 + 35296080 z + 15734775 z^2 + 66964275 z^3 - 1088732515 z^4 + 3028407889 z^5 - 3983362344 z^6 + 2846101440 z^7 - 1072081920 z^8 + 167731200 z^9) EllipticK[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[1 - z] (-32117760 + 58548000 z + 50131725 z^2 + 156981825 z^3 - 6530142905 z^4 + 20364038123 z^5 - 28534353120 z^6 + 21327371520 z^7 - 8325058560 z^8 + 1341849600 z^9) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-32117760 + 58548000 z + 50131725 z^2 + 156981825 z^3 - 6530142905 z^4 + 20364038123 z^5 - 28534353120 z^6 + 21327371520 z^7 - 8325058560 z^8 + 1341849600 z^9) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (144792971197875 Pi (1 + Sqrt[1 - z])^(1/4) (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