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

Author

Stanislav Sykora, Jun 09 2012

Keywords

• nonn
• cons

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

Examples

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

Crossrefs

Cf. A115365.

Programs

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 *)

PARI

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

PARI

-sinc(besseljzero(3/2,1)) \\ Charles R Greathouse IV, Jan 23 2025

Formula

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