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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=1, b>=a > For fixed z and a=1, b=1





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









  


  










Input Form





Hypergeometric2F1[1, 1, -(11/4), z] == (1/(616 (1 - z)^(19/4))) (616 (1 - z)^(3/4) - 2688 (1 - z)^(3/4) z + 4848 (1 - z)^(3/4) z^2 - 5856 (1 - z)^(3/4) z^3 + 2310 Sqrt[2] z^(15/4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] + 2310 Sqrt[2] z^(15/4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] + 1155 Sqrt[2] z^(15/4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] - 1155 Sqrt[2] z^(15/4) 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