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%I #5 Jun 02 2014 10:44:47
%S 2,4,4,1,3,2,3,8,1,3,6,9,4,8,3,4,5,7,4,4,6,2,0,7,8,5,1,2,6,1,4,9,1,2,
%T 3,9,0,8,0,5,0,7,8,7,3,8,3,2,7,7,3,1,4,3,5,0,5,3,7,1,3,2,5,3,8,9,9,9,
%U 2,7,3,0,0,0,6,1,2,2,7,1,0,9,9,0,5,1,1,3,4,1,6,8,7,0,9,3,7,6,4,1
%N Decimal expansion of a constant related to the asymptotic evaluation of the Lebesgue constants L_n.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.2 Lebesgue constants, p. 251.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/LebesgueConstants.html">Lebesgue constants</a>
%F 2*(sum_(k>0) log(k)/(4*k^2-1))- psi(1/2), where psi is the digamma function.
%F Equals Pi^2/4*A243277.
%e 2.441323813694834574462078512614912390805...
%t digits = 100; m0 = 50; dm = 50; Clear[f]; f[m_] := f[m] = 8/Pi^2*Sum[-Zeta'[2*k]/2^(2*k), {k, 1, m}] - 4/Pi^2*PolyGamma[1/2]; f[m0]; f[m = m0 + dm]; While[RealDigits[f[m], 10, digits + 10] != RealDigits[f[m - dm], 10, digits + 10], Print["m = ", m]; m = m + dm]; RealDigits[f[m], 10, digits] // First
%Y Cf. A226654, A226655, A226656, A243277.
%K nonn,cons
%O 1,1
%A _Jean-François Alcover_, Jun 02 2014
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