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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=-15/4





http://functions.wolfram.com/07.23.03.9104.01









  


  








Input Form





Hypergeometric2F1[-(23/4), -(15/4), -(7/4), z] == (1/28672) (8 (1 - z)^(3/4) (3584 - 41472 z + 353792 z^2 + 1102821 z^3 + 101640 z^4 - 6160 z^5) - 1009470 Sqrt[2] z^(11/4) (5 + 4 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^(11/4) (5 + 4 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^(11/4) (5 + 4 z) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 504735 Sqrt[2] z^(11/4) (5 + 4 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