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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=4





http://functions.wolfram.com/07.23.03.b11r.01









  


  








Input Form





Hypergeometric2F1[2, 4, -(29/5), z] == -((1/(2066250 (-1 + z)^11)) (2066250 - 25578750 z + 149446875 z^2 - 556040625 z^3 + 1529456250 z^4 - 3624013750 z^5 + 10668573125 z^6 + 12617559041 z^7 + 522397590 z^8 - 18265650 z^9)) - (714714 Sqrt[2 (5 + Sqrt[5])] z^(34/5) (13 + 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))])/ (3125 (1 - z)^(59/5)) - (714714 Sqrt[10 - 2 Sqrt[5]] z^(34/5) (13 + 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))])/ (3125 (1 - z)^(59/5)) + (1429428 z^(34/5) (13 + 5 z) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(3125 (1 - z)^(59/5)) + (357357 (-1 + Sqrt[5]) z^(34/5) (13 + 5 z) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(3125 (1 - z)^(59/5)) - (357357 (1 + Sqrt[5]) z^(34/5) (13 + 5 z) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(3125 (1 - z)^(59/5))








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