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A243258
Decimal expansion of a constant related to the asymptotic expansion of the smallest Lebesgue constant corresponding to an optimal interpolation data set.
2
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
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
Sequence in context: A089086 A238716 A280695 * A275704 A038631 A158625
KEYWORD
nonn,cons
AUTHOR
STATUS
approved