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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=6





http://functions.wolfram.com/07.23.03.b19e.01









  


  








Input Form





Hypergeometric2F1[2, 6, -(26/5), z] == -((1/(22343750 (-1 + z)^13)) (22343750 - 342031250 z + 2542031250 z^2 - 12517656250 z^3 + 48560546875 z^4 - 186543515625 z^5 + 2186704765625 z^6 + 2254121748169 z^7 + 85566696930 z^8 - 9315284550 z^9 + 920955750 z^10 - 49871250 z^11)) - (125234172 Sqrt[2 (5 + Sqrt[5])] z^(31/5) (36 + 25 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))])/ (390625 (1 - z)^(66/5)) - (125234172 Sqrt[10 - 2 Sqrt[5]] z^(31/5) (36 + 25 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))])/ (390625 (1 - z)^(66/5)) - (250468344 z^(31/5) (36 + 25 z) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(390625 (1 - z)^(66/5)) - (62617086 (-1 + Sqrt[5]) z^(31/5) (36 + 25 z) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(390625 (1 - z)^(66/5)) + (62617086 (1 + Sqrt[5]) z^(31/5) (36 + 25 z) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(390625 (1 - z)^(66/5))








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