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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 5 and fixed z > For fixed z and a=4, b>=a > For fixed z and a=4, b=5





http://functions.wolfram.com/07.23.03.b3km.01









  


  








Input Form





Hypergeometric2F1[4, 5, -(26/5), z] == (1/(312812500 (-1 + z)^14)) (312812500 - 5582500000 z + 49606562500 z^2 - 302303203125 z^3 + 1524890937500 z^4 - 8215686171875 z^5 + 153141879843750 z^6 + 350594621654291 z^7 + 161054811297730 z^8 + 15042847748525 z^9 + 43893349500 z^10) - (1/(390625 (1 - z)^(71/5))) (8945298 Sqrt[2 (5 + Sqrt[5])] z^(31/5) (2829 + 4715 z + 1725 z^2 + 125 z^3) ArcTan[1 - ((1 - Sqrt[5]) z^(1/5))/(4 (1 - z)^(1/5)), -((Sqrt[5/8 + Sqrt[5]/8] z^(1/5))/(1 - z)^(1/5))]) - (1/(390625 (1 - z)^(71/5))) (8945298 Sqrt[10 - 2 Sqrt[5]] z^(31/5) (2829 + 4715 z + 1725 z^2 + 125 z^3) ArcTan[1 - ((1 + Sqrt[5]) z^(1/5))/(4 (1 - z)^(1/5)), -((Sqrt[5/8 - Sqrt[5]/8] z^(1/5))/(1 - z)^(1/5))]) - (17890596 z^(31/5) (2829 + 4715 z + 1725 z^2 + 125 z^3) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(390625 (1 - z)^(71/5)) - (1/(390625 (1 - z)^(71/5))) (4472649 (-1 + Sqrt[5]) z^(31/5) (2829 + 4715 z + 1725 z^2 + 125 z^3) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)]) + (1/(390625 (1 - z)^(71/5))) (4472649 (1 + Sqrt[5]) z^(31/5) (2829 + 4715 z + 1725 z^2 + 125 z^3) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])








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