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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.b2nb.01









  


  








Input Form





Hypergeometric2F1[3, 6, -(24/5), z] == (1/(29687500 (-1 + z)^13)) (-29687500 + 497265625 z - 4173046875 z^2 + 24459375000 z^3 - 125097656250 z^4 + 834233203125 z^5 + 3878256595773 z^6 + 2009892022890 z^7 + 77373293400 z^8 - 3988000250 z^9 + 152213750 z^10) + (1/(1953125 (1 - z)^(69/5))) (93270177 Sqrt[2 (5 + Sqrt[5])] z^(29/5) (663 + 975 z + 250 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)^(69/5))) (93270177 Sqrt[10 - 2 Sqrt[5]] z^(29/5) (663 + 975 z + 250 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))]) - (186540354 z^(29/5) (663 + 975 z + 250 z^2) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(1953125 (1 - z)^(69/5)) - (93270177 (-1 + Sqrt[5]) z^(29/5) (663 + 975 z + 250 z^2) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(3906250 (1 - z)^(69/5)) + (93270177 (1 + Sqrt[5]) z^(29/5) (663 + 975 z + 250 z^2) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(3906250 (1 - z)^(69/5))








Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2007-05-02