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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=6





http://functions.wolfram.com/07.23.03.b3oa.01









  


  








Input Form





Hypergeometric2F1[4, 6, -(21/5), z] == -((1/(601562500 (-1 + z)^14)) (-601562500 + 11859375000 z - 121666015625 z^2 + 931683593750 z^3 - 7272603515625 z^4 + 192606203125000 z^5 + 642199669125077 z^6 + 447212727202290 z^7 + 69816120116725 z^8 + 484735251000 z^9 - 9542032500 z^10)) + (1/(9765625 (1 - z)^(71/5))) (116288874 Sqrt[2 (5 + Sqrt[5])] z^(26/5) (3813 + 9225 z + 5125 z^2 + 625 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/(9765625 (1 - z)^(71/5))) (116288874 Sqrt[10 - 2 Sqrt[5]] z^(26/5) (3813 + 9225 z + 5125 z^2 + 625 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))]) + (232577748 z^(26/5) (3813 + 9225 z + 5125 z^2 + 625 z^3) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(9765625 (1 - z)^(71/5)) + (1/(9765625 (1 - z)^(71/5))) (58144437 (-1 + Sqrt[5]) z^(26/5) (3813 + 9225 z + 5125 z^2 + 625 z^3) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)]) - (1/(9765625 (1 - z)^(71/5))) (58144437 (1 + Sqrt[5]) z^(26/5) (3813 + 9225 z + 5125 z^2 + 625 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