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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.b2jj.01









  


  










Input Form





Hypergeometric2F1[3, 5, -(29/5), z] == -((1/(17218750 (-1 + z)^13)) (17218750 - 268375000 z + 2033296875 z^2 - 10187062500 z^3 + 39639140625 z^4 - 141797250000 z^5 + 682669640625 z^6 + 2068942485684 z^7 + 690875065935 z^8 + 14198498600 z^9 - 334870250 z^10)) - (1/(78125 (1 - z)^(69/5))) (6432426 Sqrt[2 (5 + Sqrt[5])] z^(34/5) (429 + 440 z + 75 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)^(69/5))) (6432426 Sqrt[10 - 2 Sqrt[5]] z^(34/5) (429 + 440 z + 75 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))]) + (12864852 z^(34/5) (429 + 440 z + 75 z^2) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(78125 (1 - z)^(69/5)) + (3216213 (-1 + Sqrt[5]) z^(34/5) (429 + 440 z + 75 z^2) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(78125 (1 - z)^(69/5)) - (3216213 (1 + Sqrt[5]) z^(34/5) (429 + 440 z + 75 z^2) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(78125 (1 - z)^(69/5))










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