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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=29/8





http://functions.wolfram.com/07.23.03.b9c6.01









  


  










Input Form





Hypergeometric2F1[-(41/8), 29/8, 5, z] == (1/(693482125210875 Pi z^4)) (32768 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-117765120 + 128805600 z + 174692595 z^2 + 667374015 z^3 - 28086414335 z^4 + 93255710149 z^5 - 137466762440 z^6 + 107160951216 z^7 - 43357140288 z^8 + 7210038528 z^9) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-14720640 + 13685595 z + 23346015 z^2 - 4145125215 z^3 + 14546636405 z^4 - 22018392592 z^5 + 17461457216 z^6 - 7154661888 z^7 + 1201673088 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (14720640 - 5405235 z - 24726075 z^2 - 7155726105 z^3 + 26450806015 z^4 - 41331751688 z^5 + 33592931152 z^6 - 14051822400 z^7 + 2403346176 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-117765120 + 128805600 z + 174692595 z^2 + 667374015 z^3 - 28086414335 z^4 + 93255710149 z^5 - 137466762440 z^6 + 107160951216 z^7 - 43357140288 z^8 + 7210038528 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))










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