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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=-7/4, b>=a > For fixed z and a=-7/4, b=5/4





http://functions.wolfram.com/07.23.03.af06.01









  


  








Input Form





Hypergeometric2F1[-(7/4), 5/4, 9/4, z] == -((1/(3072 z^(5/4))) (5 (168 (1 - z)^(3/4) z^(1/4) - 480 (1 - z)^(3/4) z^(5/4) + 256 (1 - z)^(3/4) z^(9/4) + 42 Sqrt[2] ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] + 42 Sqrt[2] ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] + 21 Sqrt[2] Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] - 21 Sqrt[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