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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/07.23.03.9468.01









  


  








Input Form





Hypergeometric2F1[-(23/4), 1/4, 5/4, z] == (1/7864320) (8 (1 - z)^(3/4) (478305 - 797004 z + 929952 z^2 - 653952 z^3 + 251904 z^4 - 40960 z^5) - (1009470 Sqrt[2] ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/z^(1/4) - (1009470 Sqrt[2] ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/z^(1/4) - (504735 Sqrt[2] Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/z^(1/4) + (504735 Sqrt[2] Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/z^(1/4))








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