A243258 - OEIS

%I #13 Sep 08 2022 08:46:08

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

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

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

%N Decimal expansion of a constant related to the asymptotic expansion of the smallest Lebesgue constant corresponding to an optimal interpolation data set.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.2 Lebesgue constants, p. 254.

%H G. C. Greubel, <a href="/A243258/b243258.txt">Table of n, a(n) for n = 0..10000</a>

%H P. Vértesi, <a href="http://dx.doi.org/10.1137/0727075">Optimal Lebesgue constant for Lagrange interpolation</a>, SIAM J. Numer. Anal., 27(5), 1322-1331.

%F Equals 2/Pi*(2*log(2) - log(Pi) + gamma), where gamma is the Euler-Mascheroni constant.

%e 0.5212516264554098210052192041271783...

%t RealDigits[2/Pi*(2*Log[2] - Log[Pi] + EulerGamma), 10, 104] // First

%o (PARI) default(realprecision, 100); (2/Pi)*(2*log(2) - log(Pi) + Euler) \\ _G. C. Greubel_, Sep 04 2018

%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (2/Pi(R))*(2*Log(2) - Log(Pi(R)) + EulerGamma(R)); // _G. C. Greubel_, Sep 04 2018

%Y Cf. A243257, A001620.

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Jun 02 2014