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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=4





http://functions.wolfram.com/07.23.03.b2fz.01









  


  








Input Form





Hypergeometric2F1[3, 4, -(19/5), z] == (1/(1246875 (-1 + z)^10)) (1246875 - 16406250 z + 109546875 z^2 - 545562500 z^3 + 3173796875 z^4 + 10567072338 z^5 + 3210875775 z^6 + 39341400 z^7) - (1/(15625 (1 - z)^(54/5))) (76908 Sqrt[2 (5 + Sqrt[5])] z^(24/5) (493 + 510 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/(15625 (1 - z)^(54/5))) (76908 Sqrt[10 - 2 Sqrt[5]] z^(24/5) (493 + 510 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))]) + (153816 z^(24/5) (493 + 510 z + 75 z^2) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(15625 (1 - z)^(54/5)) + (38454 (-1 + Sqrt[5]) z^(24/5) (493 + 510 z + 75 z^2) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(15625 (1 - z)^(54/5)) - (38454 (1 + Sqrt[5]) z^(24/5) (493 + 510 z + 75 z^2) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(15625 (1 - z)^(54/5))








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