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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.b15j.01









  


  










Input Form





Hypergeometric2F1[2, 5, -(29/5), z] == (1/(6887500 (-1 + z)^12)) (6887500 - 94525000 z + 619340625 z^2 - 2620875000 z^3 + 8342906250 z^4 - 23356462500 z^5 + 82864753125 z^6 + 134790428244 z^7 + 9162050040 z^8 - 633209200 z^9 + 30442750 z^10) - (3216213 Sqrt[2 (5 + Sqrt[5])] z^(34/5) (39 + 20 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)^(64/5)) - (3216213 Sqrt[10 - 2 Sqrt[5]] z^(34/5) (39 + 20 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)^(64/5)) + (6432426 z^(34/5) (39 + 20 z) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(15625 (1 - z)^(64/5)) + (3216213 (-1 + Sqrt[5]) z^(34/5) (39 + 20 z) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(31250 (1 - z)^(64/5)) - (3216213 (1 + Sqrt[5]) z^(34/5) (39 + 20 z) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(31250 (1 - z)^(64/5))










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