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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=3, b>=a > For fixed z and a=3, b=5





http://functions.wolfram.com/07.23.03.b2jq.01









  


  








Input Form





Hypergeometric2F1[3, 5, -(21/5), z] == -((1/(4812500 (-1 + z)^12)) (-4812500 + 74937500 z - 588328125 z^2 + 3308359375 z^3 - 17936875000 z^4 + 305405250000 z^5 + 556168059541 z^6 + 154791603185 z^7 + 1703601900 z^8 - 46546500 z^9)) + (1/(78125 (1 - z)^(61/5))) (6840522 Sqrt[2 (5 + Sqrt[5])] z^(26/5) (93 + 120 z + 25 z^2) 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/(78125 (1 - z)^(61/5))) (6840522 Sqrt[10 - 2 Sqrt[5]] z^(26/5) (93 + 120 z + 25 z^2) 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))]) + (13681044 z^(26/5) (93 + 120 z + 25 z^2) Log[1 + z^(1/5)/(1 - z)^(1/5)])/ (78125 (1 - z)^(61/5)) + (3420261 (-1 + Sqrt[5]) z^(26/5) (93 + 120 z + 25 z^2) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(78125 (1 - z)^(61/5)) - (3420261 (1 + Sqrt[5]) z^(26/5) (93 + 120 z + 25 z^2) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(78125 (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