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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.b2ju.01









  


  








Input Form





Hypergeometric2F1[3, 5, -(16/5), z] == -((1/(2750000 (-1 + z)^11)) (2750000 - 43140625 z + 363359375 z^2 - 2619765625 z^3 + 55436796875 z^4 + 121642486082 z^5 + 39629063270 z^6 + 505805300 z^7 - 15515500 z^8)) - (1/(78125 (1 - z)^(56/5))) (1040949 Sqrt[(1/2) (5 + Sqrt[5])] z^(21/5) (403 + 620 z + 150 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)^(56/5))) (1040949 Sqrt[(1/2) (5 - Sqrt[5])] z^(21/5) (403 + 620 z + 150 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))]) - (1040949 z^(21/5) (403 + 620 z + 150 z^2) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(78125 (1 - z)^(56/5)) - (1040949 (-1 + Sqrt[5]) z^(21/5) (403 + 620 z + 150 z^2) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(312500 (1 - z)^(56/5)) + (1040949 (1 + Sqrt[5]) z^(21/5) (403 + 620 z + 150 z^2) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(312500 (1 - z)^(56/5))








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