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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=-15/4, b>=a > For fixed z and a=-15/4, b=1/4





http://functions.wolfram.com/07.23.03.abb9.01









  


  








Input Form





Hypergeometric2F1[-(15/4), 1/4, 9/4, z] == (1/(262144 z^(5/4))) (8 (1 - z)^(3/4) z^(1/4) (1155 + 10592 z - 6736 z^2 + 2816 z^3 - 512 z^4) - 2310 Sqrt[2] (-1 + 20 z) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 2310 Sqrt[2] (-1 + 20 z) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 1155 Sqrt[2] (-1 + 20 z) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 1155 Sqrt[2] (-1 + 20 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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</annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02