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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.b3h3.01









  


  








Input Form





Hypergeometric2F1[4, 4, -(19/5), z] == -((1/(6234375 (-1 + z)^11)) (6234375 - 94828125 z + 748828125 z^2 - 4542734375 z^3 + 33390546875 z^4 + 166848843519 z^5 + 93820050365 z^6 + 7541464225 z^7)) - (1/(78125 (1 - z)^(59/5))) (76908 Sqrt[2 (5 + Sqrt[5])] z^(24/5) (6409 + 9945 z + 2925 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)^(59/5))) (76908 Sqrt[10 - 2 Sqrt[5]] z^(24/5) (6409 + 9945 z + 2925 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))]) + (153816 z^(24/5) (6409 + 9945 z + 2925 z^2 + 125 z^3) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(78125 (1 - z)^(59/5)) + (1/(78125 (1 - z)^(59/5))) (38454 (-1 + Sqrt[5]) z^(24/5) (6409 + 9945 z + 2925 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)^(59/5))) (38454 (1 + Sqrt[5]) z^(24/5) (6409 + 9945 z + 2925 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