A272335 Decimal expansion of a function approximation constant which is the analog of Gibbs's constant 2*G/Pi (A036793) for de la Vallée-Poussin sums.

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

Offset

1,3

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.1 Gibbs-Wilbraham Constant, p. 248.

Links

Table of n, a(n) for n=1..101.

R. P. Boyer and W. M. Y. Goh Generalized Gibbs phenomenon for Fourier partial sums and de la Vallée-Poussin sums, J. Appl. Math. Comput. 37 (2011) 421-442, p. 11.

Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020-2024; p. 33.

Formula

Equals (2/Pi)*Integral_{t=0..2*Pi/3} (cos(t) - cos(2*t))/t^2 dt.

Equals (2/Pi)*(2*Si(4*Pi/3) - Si(2*Pi/3)), where Si is the Sine integral function.

Example

1.14272812693068128481021845956657111930110150452947023957171253...

Mathematica

(2/Pi)(2 SinIntegral[4 Pi/3] - SinIntegral[2 Pi/3]) // N[#, 101]& // RealDigits // First

Crossrefs

Cf. A036792, A036793, A243267, A243268, A245535.

Sequence in context: A076129 A260590 A010648 * A198994 A368664 A182364

Adjacent sequences: A272332 A272333 A272334 * A272336 A272337 A272338

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 26 2016

Status

approved