A213053 Decimal expansion of the absolute minimum of sinc(x) = sin(x)/x (negated).

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

Offset

0,1

Comments

Minimum value of the first negative lobe of sinc(x), attained for abs(x) = A115365.

The involute of the unit circle which starts at (1,0) crosses the x-axis for the first time at x = 1/a. - Álvar Ibeas, Jul 28 2017

Links

Table of n, a(n) for n=0..104.

Formula

Equals -1 / sqrt(1 + A115365^2) = cos(A115365). - Álvar Ibeas, Jul 28 2017

Example

min[real x](sinc(x)) = -0.2172336282112216574082...

Mathematica

digits = 105; NMinimize[ Sinc[x], x, WorkingPrecision -> digits+5] // First // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Mar 05 2013 *)
RealDigits[Sinc[BesselJZero[3/2, 1]], 10, 100][[1]] (* Vladimir Reshetnikov, May 13 2016 *)

Prog

(PARI) y=solve(x=4, 4.5, tan(x)-x); -sin(y)/y \\ Charles R Greathouse IV, Jun 10 2012

Crossrefs

Cf. A115365.

Sequence in context: A121416 A317547 A089329 * A200236 A292191 A239155

Adjacent sequences: A213050 A213051 A213052 * A213054 A213055 A213056

Keyword

nonn,cons

Author

Stanislav Sykora, Jun 09 2012

Status

approved