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A243277 Decimal expansion of 'c', a constant related to the asymptotic evaluation of the Lebesgue constants L_n. 2

%I #6 Jun 02 2014 10:45:00

%S 9,8,9,4,3,1,2,7,3,8,3,1,1,4,6,9,5,1,7,4,1,6,4,8,8,0,9,0,1,8,8,6,6,7,

%T 1,4,9,2,4,2,0,1,4,0,6,0,9,1,1,1,1,0,4,8,2,8,4,1,2,2,4,3,2,6,4,4,3,7,

%U 2,5,3,1,5,8,4,5,7,8,6,5,4,6,3,4,6,3,2,9,8,3,1,4,0,1,8,9,5,5,7,9

%N Decimal expansion of 'c', 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 c = limit_(n->infinity) (L_n - 4/Pi^2*log(2*n+1)).

%F c = 8/Pi^2*(sum_(k>0) log(k)/(4*k^2-1))-4/Pi^2*psi(1/2), where psi is the digamma function.

%F c = 4/Pi^2*A243278.

%e 0.9894312738311469517416488090188667149242...

%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, A243278.

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Jun 02 2014

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