A243277 - OEIS

A243277

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

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, 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, 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

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OFFSET

0,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.2 Lebesgue constants, p. 251.

LINKS

Table of n, a(n) for n=0..99.

Eric Weisstein's MathWorld, Lebesgue constants

FORMULA

c = limit_(n->infinity) (L_n - 4/Pi^2*log(2*n+1)).

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.

c = 4/Pi^2*A243278.

EXAMPLE

0.9894312738311469517416488090188667149242...

MATHEMATICA

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

CROSSREFS

Cf. A226654, A226655, A226656, A243278.

Sequence in context: A245330 A269222 A201994 * A200003 A159590 A309642

Adjacent sequences: A243274 A243275 A243276 * A243278 A243279 A243280

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Jun 02 2014

STATUS

approved