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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=2, b>=a > For fixed z and a=2, b=2





http://functions.wolfram.com/07.23.03.akt9.01









  


  








Input Form





Hypergeometric2F1[2, 2, -(7/4), z] == (1/896) (-((8 (112 - 816 z + 3936 z^2 + 4083 z^3))/(-1 + z)^5) - (2310 Sqrt[2] z^(11/4) (15 + 4 z) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(23/4) - (2310 Sqrt[2] z^(11/4) (15 + 4 z) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(23/4) - (1155 Sqrt[2] z^(11/4) (15 + 4 z) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(23/4) + (1155 Sqrt[2] z^(11/4) (15 + 4 z) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(23/4))








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