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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 (list; constant; graph; refs; listen; history; text; internal format)
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

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Last modified January 18 13:09 EST 2019. Contains 319271 sequences. (Running on oeis4.)