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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/07.23.03.9020.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(19/4), -(7/4), z] == (1/229376) (8 (1 - z)^(3/4) (28672 - 425984 z + 4997120 z^2 + 28825599 z^3 + 13280868 z^4 + 234080 z^5) - 1009470 Sqrt[2] z^(11/4) (95 + 152 z + 32 z^2) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 1009470 Sqrt[2] z^(11/4) (95 + 152 z + 32 z^2) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 504735 Sqrt[2] z^(11/4) (95 + 152 z + 32 z^2) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 504735 Sqrt[2] z^(11/4) (95 + 152 z + 32 z^2) 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