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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=4





http://functions.wolfram.com/07.23.03.b3h6.01









  


  








Input Form





Hypergeometric2F1[4, 4, -(16/5), z] == -((1/(687500 (-1 + z)^11)) (687500 - 11000000 z + 95156250 z^2 - 712656250 z^3 + 15979609375 z^4 + 38995236399 z^5 + 16263155135 z^6 + 1023757975 z^7)) - (1/(78125 (1 - z)^(56/5))) (50778 Sqrt[2 (5 + Sqrt[5])] z^(21/5) (4836 + 8370 z + 2700 z^2 + 125 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/(78125 (1 - z)^(56/5))) (50778 Sqrt[10 - 2 Sqrt[5]] z^(21/5) (4836 + 8370 z + 2700 z^2 + 125 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))]) - (101556 z^(21/5) (4836 + 8370 z + 2700 z^2 + 125 z^3) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(78125 (1 - z)^(56/5)) - (1/(78125 (1 - z)^(56/5))) (25389 (-1 + Sqrt[5]) z^(21/5) (4836 + 8370 z + 2700 z^2 + 125 z^3) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)]) + (1/(78125 (1 - z)^(56/5))) (25389 (1 + Sqrt[5]) z^(21/5) (4836 + 8370 z + 2700 z^2 + 125 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