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%I #7 Jul 17 2015 05:16:23
%S 1,2,7,0,3,5,3,2,4,4,9,2,1,8,7,8,4,5,7,3,7,7,4,0,3,2,0,7,0,0,6,8,5,4,
%T 7,5,3,4,5,5,7,0,7,5,3,5,8,6,4,1,6,1,2,1,3,7,9,3,8,5,9,9,4,5,5,5,7,3,
%U 7,1,0,9,6,9,3,2,4,5,2,7,9,0,6,9,1,4,3,9,7,5,7,4,6,3,1,2,3,1,6,1,7,0,6
%N Decimal expansion of the constant c_0 appearing in the asymptotic evaluation of the n-th Lebesgue constant (related to Fourier series) as L_n ~ (4/Pi^2)*log(n) + c_0.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.2 Lebesgue constants, p. 251.
%H Leopold Fejér, <a href="http://eudml.org/doc/149327">Lebesguesche Konstanten und divergente Fourierreihen</a>, Journal für die reine und angewandte Mathematik, Vol. 138 (1910), page 30.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/LebesgueConstants.html">Lebesgue constants</a>
%F c_0 = 2*Integral_{0..1} cos(Pi*t)*LogGamma(t) dt + 4*log(4/Pi)/Pi^2.
%F Also equals A243277 + log(16)/Pi^2 or (4/Pi^2)*(A243278 + log(2)).
%e c_0 = 1.270353244921878457377403207006854753455707535864161213793859945557371...
%e Integral_{0..1} cos(Pi*t)*LogGamma(t) dt =
%e 0.58622542534024658158560382093726746382526606396195055488919749303076...
%t c0 = 2*NIntegrate[Cos[Pi*t]*LogGamma[t], {t, 0, 1}, WorkingPrecision -> 103] + 4*Log[4/Pi]/Pi^2 ; RealDigits[c0] // First
%Y Cf. A157165, A157166, A157167, A157168, A226654, A226655, A226656, A243277, A243278.
%K nonn,cons,easy
%O 1,2
%A _Jean-François Alcover_, Jul 17 2015
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