A245535 Decimal expansion of the analog of the Gibbs-Wilbraham constant for L_1 trigonometric polynomial approximation.

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

Offset

0,2

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.1 Gibbs-Wilbraham Constant, p. 249.

Links

Table of n, a(n) for n=0..101.

Eric Weisstein's MathWorld, Wilbraham-Gibbs Constant

Formula

Maximum g(x0) of the function g(x) = (psi(x/2) - psi((x+1)/2) + 1/x)*sin(Pi*x)/Pi, for x >= 1, where psi is the polygamma function.

Example

x0 = 1.376991769203938865765266614301624670814900061506257246...
g(x0) = 0.0657838882664480990565512180874704669499564803216...

Mathematica

digits = 101; g[x_] := (PolyGamma[x/2] - PolyGamma[(x+1)/2] + 1/x)*Sin[Pi*x]/Pi; x0 = x /. FindRoot[g'[x] == 0, {x, 3/2}, WorkingPrecision -> digits+5]; RealDigits[g[x0], 10, digits] // First

Crossrefs

Cf. A036792, A036793, A243267, A243268.

Sequence in context: A365927 A196400 A086268 * A191102 A021156 A182448

Adjacent sequences: A245532 A245533 A245534 * A245536 A245537 A245538

Keyword

nonn,cons

Author

Jean-François Alcover, Jul 25 2014

Status

approved