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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=6





http://functions.wolfram.com/07.23.03.b2ne.01









  


  








Input Form





Hypergeometric2F1[3, 6, -(21/5), z] == (1/(120312500 (-1 + z)^13)) (-120312500 + 2079687500 z - 18343359375 z^2 + 117626171875 z^3 - 740992187500 z^4 + 15001209375000 z^5 + 34035175599091 z^6 + 12573987875045 z^7 + 216078162300 z^8 - 11776264500 z^9 + 465465000 z^10) + (1/(1953125 (1 - z)^(66/5))) (116288874 Sqrt[2 (5 + Sqrt[5])] z^(26/5) (279 + 450 z + 125 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/(1953125 (1 - z)^(66/5))) (116288874 Sqrt[10 - 2 Sqrt[5]] z^(26/5) (279 + 450 z + 125 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))]) + (232577748 z^(26/5) (279 + 450 z + 125 z^2) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(1953125 (1 - z)^(66/5)) + (58144437 (-1 + Sqrt[5]) z^(26/5) (279 + 450 z + 125 z^2) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(1953125 (1 - z)^(66/5)) - (58144437 (1 + Sqrt[5]) z^(26/5) (279 + 450 z + 125 z^2) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(1953125 (1 - z)^(66/5))








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