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

Author

Jean-François Alcover, Apr 26 2016

Keywords

• nonn
• cons

Examples

			1.14272812693068128481021845956657111930110150452947023957171253...
		

References

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

Links

• 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.

Crossrefs

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

Programs

Mathematica

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

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.