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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=2, b>=a > For fixed z and a=2, b=5





http://functions.wolfram.com/07.23.03.b15m.01









  


  








Input Form





Hypergeometric2F1[2, 5, -(26/5), z] == (1/(12512500 (-1 + z)^12)) (12512500 - 174212500 z + 1166137500 z^2 - 5110015625 z^3 + 17378843750 z^4 - 57445837500 z^5 + 567060456250 z^6 + 467961611261 z^7 + 12919446540 z^8 - 940239300 z^9 + 46546500 z^10) - (8945298 Sqrt[2 (5 + Sqrt[5])] z^(31/5) (9 + 5 z) 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))])/ (15625 (1 - z)^(61/5)) - (8945298 Sqrt[10 - 2 Sqrt[5]] z^(31/5) (9 + 5 z) 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))])/ (15625 (1 - z)^(61/5)) - (17890596 z^(31/5) (9 + 5 z) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(15625 (1 - z)^(61/5)) - (4472649 (-1 + Sqrt[5]) z^(31/5) (9 + 5 z) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(15625 (1 - z)^(61/5)) + (4472649 (1 + Sqrt[5]) z^(31/5) (9 + 5 z) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(15625 (1 - z)^(61/5))








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