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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=6





http://functions.wolfram.com/07.23.03.b3oe.01









  


  








Input Form





Hypergeometric2F1[4, 6, -(16/5), z] == -((1/(85937500 (-1 + z)^13)) (85937500 - 1761718750 z + 20208984375 z^2 - 209861328125 z^3 + 6917656250000 z^4 + 27766105360566 z^5 + 22608399283945 z^6 + 4043278194425 z^7 + 31977445500 z^8 - 698197500 z^9)) - (1/(9765625 (1 - z)^(66/5))) (47883654 Sqrt[2 (5 + Sqrt[5])] z^(21/5) (2418 + 6975 z + 4500 z^2 + 625 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/(9765625 (1 - z)^(66/5))) (47883654 Sqrt[10 - 2 Sqrt[5]] z^(21/5) (2418 + 6975 z + 4500 z^2 + 625 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))]) - (95767308 z^(21/5) (2418 + 6975 z + 4500 z^2 + 625 z^3) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(9765625 (1 - z)^(66/5)) - (1/(9765625 (1 - z)^(66/5))) (23941827 (-1 + Sqrt[5]) z^(21/5) (2418 + 6975 z + 4500 z^2 + 625 z^3) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)]) + (1/(9765625 (1 - z)^(66/5))) (23941827 (1 + Sqrt[5]) z^(21/5) (2418 + 6975 z + 4500 z^2 + 625 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