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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.
0
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
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.
FORMULA
(2/Pi)*Integral_{t=0..2*Pi/3} ((cos(t) - cos(2*t))/t^2.
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
KEYWORD
nonn,cons
AUTHOR
STATUS
approved