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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=2, b>=a > For fixed z and a=2, b=5





http://functions.wolfram.com/07.23.03.b162.01









  


  








Input Form





Hypergeometric2F1[2, 5, -(6/5), z] == (9375 - 153125 z + 4403125 z^2 + 8688637 z^3 + 518980 z^4 - 67100 z^5 + 5500 z^6)/(9375 (-1 + z)^8) - (248248 Sqrt[2 (5 + Sqrt[5])] z^(11/5) (4 + 5 z) 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))])/ (15625 (1 - z)^(41/5)) - (248248 Sqrt[10 - 2 Sqrt[5]] z^(11/5) (4 + 5 z) 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))])/ (15625 (1 - z)^(41/5)) - (496496 z^(11/5) (4 + 5 z) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(15625 (1 - z)^(41/5)) - (124124 (-1 + Sqrt[5]) z^(11/5) (4 + 5 z) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(15625 (1 - z)^(41/5)) + (124124 (1 + Sqrt[5]) z^(11/5) (4 + 5 z) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(15625 (1 - z)^(41/5))








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