A243278 Decimal expansion of a constant related to the asymptotic evaluation of the Lebesgue constants L_n.

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

Offset

1,1

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=1..100.

Eric Weisstein's MathWorld, Lebesgue constants

Formula

2*(sum_(k>0) log(k)/(4*k^2-1))- psi(1/2), where psi is the digamma function.

Equals Pi^2/4*A243277.

Example

2.441323813694834574462078512614912390805...

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, A243277.

Sequence in context: A140734 A295633 A159778 * A307059 A328412 A079536

Adjacent sequences: A243275 A243276 A243277 * A243279 A243280 A243281

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 02 2014

Status

approved