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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 4 and fixed z > For fixed z and a=-23/4, b>=a > For fixed z and a=-23/4, b=1/4





http://functions.wolfram.com/07.23.03.9484.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 1/4, 21/4, z] == (1/(92358976733184 z^(17/4))) (221 (-8 (1 - z)^(3/4) z^(1/4) (19684665 - 226525068 z + 1273816544 z^2 - 5198635904 z^3 - 12898873344 z^4 + 6262046720 z^5 - 2779971584 z^6 + 897318912 z^7 - 180355072 z^8 + 16777216 z^9) - 3028410 Sqrt[2] (13 - 160 z + 960 z^2 - 4096 z^3 + 28672 z^4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 3028410 Sqrt[2] (13 - 160 z + 960 z^2 - 4096 z^3 + 28672 z^4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 1514205 Sqrt[2] (13 - 160 z + 960 z^2 - 4096 z^3 + 28672 z^4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 1514205 Sqrt[2] (13 - 160 z + 960 z^2 - 4096 z^3 + 28672 z^4) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/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