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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=4, b>=a > For fixed z and a=4, b=6





http://functions.wolfram.com/07.23.03.b3o6.01









  


  








Input Form





Hypergeometric2F1[4, 6, -(26/5), z] == -((1/(558593750 (-1 + z)^15)) (558593750 - 10957031250 z + 108066406250 z^2 - 739707031250 z^3 + 4253642578125 z^4 - 26618716796875 z^5 + 589892119140625 z^6 + 1681104137945289 z^7 + 1022304500578280 z^8 + 141560139742700 z^9 + 874731750750 z^10 - 15676196250 z^11)) - (1/(9765625 (1 - z)^(76/5))) (125234172 Sqrt[2 (5 + Sqrt[5])] z^(31/5) (11316 + 23575 z + 11500 z^2 + 1250 z^3) 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/(9765625 (1 - z)^(76/5))) (125234172 Sqrt[10 - 2 Sqrt[5]] z^(31/5) (11316 + 23575 z + 11500 z^2 + 1250 z^3) 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))]) - (250468344 z^(31/5) (11316 + 23575 z + 11500 z^2 + 1250 z^3) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(9765625 (1 - z)^(76/5)) - (1/(9765625 (1 - z)^(76/5))) (62617086 (-1 + Sqrt[5]) z^(31/5) (11316 + 23575 z + 11500 z^2 + 1250 z^3) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)]) + (1/(9765625 (1 - z)^(76/5))) (62617086 (1 + Sqrt[5]) z^(31/5) (11316 + 23575 z + 11500 z^2 + 1250 z^3) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])








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