A243258 Decimal expansion of a constant related to the asymptotic expansion of the smallest Lebesgue constant corresponding to an optimal interpolation data set.

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, 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, 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

Offset

0,1

References

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

P. Vértesi, Optimal Lebesgue constant for Lagrange interpolation, SIAM J. Numer. Anal., 27(5), 1322-1331.

Formula

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

Example

0.5212516264554098210052192041271783...

Mathematica

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

Prog

(PARI) default(realprecision, 100); (2/Pi)*(2*log(2) - log(Pi) + Euler) \\ G. C. Greubel, Sep 04 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (2/Pi(R))*(2*Log(2) - Log(Pi(R)) + EulerGamma(R)); // G. C. Greubel, Sep 04 2018

Crossrefs

Cf. A243257, A001620.

Sequence in context: A089086 A238716 A280695 * A275704 A038631 A158625

Adjacent sequences: A243255 A243256 A243257 * A243259 A243260 A243261

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 02 2014

Status

approved