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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=-19/4





http://functions.wolfram.com/07.23.03.9018.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(19/4), -(11/4), z] == (1/78848) (-8 (1 - z)^(3/4) (-9856 + 90496 z - 431232 z^2 + 1968000 z^3 + 2837427 z^4 + 87780 z^5) + 1009470 Sqrt[2] z^(15/4) (19 + 8 z) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] + 1009470 Sqrt[2] z^(15/4) (19 + 8 z) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] + 504735 Sqrt[2] z^(15/4) (19 + 8 z) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] - 504735 Sqrt[2] z^(15/4) (19 + 8 z) 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