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%I #6 Jul 25 2014 13:42:39
%S 0,6,5,7,8,3,8,8,8,2,6,6,4,4,8,0,9,9,0,5,6,5,5,1,2,1,8,0,8,7,4,7,0,4,
%T 6,6,9,4,9,9,5,6,4,8,0,3,2,1,6,0,5,1,2,7,3,0,7,1,3,2,0,4,7,5,3,5,4,7,
%U 9,5,3,9,7,2,9,6,1,7,7,0,4,0,8,5,8,7,1,0,5,8,8,9,9,7,8,4,5,3,3,7,9,5
%N Decimal expansion of the analog of the Gibbs-Wilbraham constant for L_1 trigonometric polynomial approximation.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.1 Gibbs-Wilbraham Constant, p. 249.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Wilbraham-GibbsConstant.html">Wilbraham-Gibbs Constant</a>
%F Maximum g(x0) of the function g(x) = (psi(x/2) - psi((x+1)/2) + 1/x)*sin(Pi*x)/Pi, for x >= 1, where psi is the polygamma function.
%e x0 = 1.376991769203938865765266614301624670814900061506257246...
%e g(x0) = 0.0657838882664480990565512180874704669499564803216...
%t digits = 101; g[x_] := (PolyGamma[x/2] - PolyGamma[(x+1)/2] + 1/x)*Sin[Pi*x]/Pi; x0 = x /. FindRoot[g'[x] == 0, {x, 3/2}, WorkingPrecision -> digits+5]; RealDigits[g[x0], 10, digits] // First
%Y Cf. A036792, A036793, A243267, A243268.
%K nonn,cons
%O 0,2
%A _Jean-François Alcover_, Jul 25 2014
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