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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.b2fr.01









  


  








Input Form





Hypergeometric2F1[3, 4, -(29/5), z] == (1/(10331250 (-1 + z)^12)) (10331250 - 145350000 z + 982893750 z^2 - 4335187500 z^3 + 14601234375 z^4 - 44302037500 z^5 + 177131325000 z^6 + 394626355152 z^7 + 87961957375 z^8 + 803688600 z^9) - (1/(15625 (1 - z)^(64/5))) (714714 Sqrt[2 (5 + Sqrt[5])] z^(34/5) (286 + 220 z + 25 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)^(64/5))) (714714 Sqrt[10 - 2 Sqrt[5]] z^(34/5) (286 + 220 z + 25 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))]) + (1429428 z^(34/5) (286 + 220 z + 25 z^2) Log[1 + z^(1/5)/(1 - z)^(1/5)])/ (15625 (1 - z)^(64/5)) + (357357 (-1 + Sqrt[5]) z^(34/5) (286 + 220 z + 25 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)^(64/5)) - (357357 (1 + Sqrt[5]) z^(34/5) (286 + 220 z + 25 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)^(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