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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=-15/4





http://functions.wolfram.com/07.23.03.ab0t.01









  


  








Input Form





Hypergeometric2F1[-(15/4), -(15/4), 5/4, z] == (1/33554432) (152 (1 - z)^(3/4) (150541 + 1095012 z + 1081248 z^2 + 143744 z^3) - (1/z^(1/4)) (2310 Sqrt[2] (1155 + 24640 z + 63360 z^2 + 30720 z^3 + 2048 z^4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) - (1/z^(1/4)) (2310 Sqrt[2] (1155 + 24640 z + 63360 z^2 + 30720 z^3 + 2048 z^4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) - (1155 Sqrt[2] (1155 + 24640 z + 63360 z^2 + 30720 z^3 + 2048 z^4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ z^(1/4) + (1155 Sqrt[2] (1155 + 24640 z + 63360 z^2 + 30720 z^3 + 2048 z^4) 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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</semantics> </math>










Rule Form





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





2007-05-02