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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=5, b>=a > For fixed z and a=5, b=5





http://functions.wolfram.com/07.23.03.b486.01









  


  








Input Form





Hypergeometric2F1[5, 5, -(6/5), z] == -((1/(4687500 (-1 + z)^11)) (4687500 - 149218750 z + 10121093750 z^2 + 72417294977 z^3 + 98890137025 z^4 + 31890894025 z^5 + 1726950625 z^6)) - (1/(1953125 (1 - z)^(56/5))) (62062 Sqrt[2 (5 + Sqrt[5])] z^(11/5) (11284 + 56420 z + 60450 z^2 + 15500 z^3 + 625 z^4) 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)^(56/5))) (62062 Sqrt[10 - 2 Sqrt[5]] z^(11/5) (11284 + 56420 z + 60450 z^2 + 15500 z^3 + 625 z^4) 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))]) - (124124 z^(11/5) (11284 + 56420 z + 60450 z^2 + 15500 z^3 + 625 z^4) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(1953125 (1 - z)^(56/5)) - (1/(1953125 (1 - z)^(56/5))) (31031 (-1 + Sqrt[5]) z^(11/5) (11284 + 56420 z + 60450 z^2 + 15500 z^3 + 625 z^4) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)]) + (1/(1953125 (1 - z)^(56/5))) (31031 (1 + Sqrt[5]) z^(11/5) (11284 + 56420 z + 60450 z^2 + 15500 z^3 + 625 z^4) 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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Date Added to functions.wolfram.com (modification date)





2007-05-02