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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.b3gv.01









  


  








Input Form





Hypergeometric2F1[4, 4, -(29/5), z] == -((1/(154968750 (-1 + z)^13)) (154968750 - 2442093750 z + 18758343750 z^2 - 95654343750 z^3 + 380987578125 z^4 - 1407050640625 z^5 + 7084868875000 z^6 + 23739834677448 z^7 + 9823822780105 z^8 + 606173327075 z^9)) - (1/(78125 (1 - z)^(69/5))) (238238 Sqrt[2 (5 + Sqrt[5])] z^(34/5) (14014 + 16170 z + 3675 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)^(69/5))) (238238 Sqrt[10 - 2 Sqrt[5]] z^(34/5) (14014 + 16170 z + 3675 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))]) + (476476 z^(34/5) (14014 + 16170 z + 3675 z^2 + 125 z^3) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(78125 (1 - z)^(69/5)) + (1/(78125 (1 - z)^(69/5))) (119119 (-1 + Sqrt[5]) z^(34/5) (14014 + 16170 z + 3675 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)^(69/5))) (119119 (1 + Sqrt[5]) z^(34/5) (14014 + 16170 z + 3675 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