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%I #46 Sep 08 2022 08:45:51
%S 5,5,6,6,3,1,6,0,0,1,7,8,0,2,3,5,2,0,4,2,5,0,0,9,6,8,9,5,2,0,7,7,2,6,
%T 1,1,1,3,9,8,7,9,9,1,1,4,8,7,2,8,5,3,4,6,1,6,1,6,7,4,4,6,2,6,3,2,2,9,
%U 0,7,5,0,2,8,1,7,8,0,2,3,0,5,5,0,3,3,8,9,6,5,3,6,2,1,0,2,1,7,5,4,6,5,9,8,1
%N Decimal expansion of Gamma(1/6).
%C A175379 * A073005 * A002161 * A073006 * A203145 = 4*sqrt(Pi^5/3), which is the case n=6 of Product_{i=1..n-1} Gamma(i/n) = sqrt((2*Pi)^(n-1)/n). - _Bruno Berselli_, Dec 18 2012
%C The transcendence of this constant is in the mathematical folklore; see Finch (who credits Nesterenko) and Gun-Murty-Rath. - _Charles R Greathouse IV_, Nov 11 2013
%H G. C. Greubel, <a href="/A175379/b175379.txt">Table of n, a(n) for n = 1..5000</a>
%H Steven Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and addenda to Mathematical Constants</a> (2013)
%H Sanoli Gun, M. Ram Murty, and Purusottam Rath, <a href="http://www.mast.queensu.ca/~murty/gun-murty-rath2.pdf">Transcendence of the log gamma function and some discrete periods</a>, J. Number Theory (2009), doi:10.1016/j.jnt.2009.01.008
%H R. Vidunas, <a href="http://arxiv.org/abs/math/0403510">Expressions for values of the Gamma function</a>, arxiv:math/0403510 [math.CA], 2004.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Particular_values_of_the_Gamma_function#General_rational_arguments">Particular values of the Gamma function: General rational arguments</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%H <a href="/index/Ga#gamma_function">Index entries to sequences related to the Gamma function</a>
%F Equals 2*Pi/A203145 = A002194 * A073005^2 / (A002161 * A002580) = A019692 / 1.12878703....
%e Equals 5.56631600178023...
%p evalf(GAMMA(1/6)) ;
%t RealDigits[Gamma[1/6], 10, 110][[1]] (* _Bruno Berselli_, Dec 13 2012 *)
%o (PARI) gamma(1/6) \\ _Charles R Greathouse IV_, Nov 16 2013
%o (Magma) SetDefaultRealField(RealField(100)); Gamma(1/6); // _G. C. Greubel_, Mar 10 2018
%Y Cf. A073006, A203145.
%K cons,nonn
%O 1,1
%A _R. J. Mathar_, Apr 24 2010
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