A211269 Integral of a sinc-shaped peak with unit height and unit half-height width.

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

Offset

0,1

Comments

See first the general introduction in A211268.

This constant is the integral from -inf to +inf under a canonical sinc-shaped spectral peak S(x) defined by S(x)=sinc(2*x*eta), with sinc(z)=sin(z)/z, and eta=A199460, so that S(0)=1 and S(+1/2)=S(-1/2)=1/2.

Links

Table of n, a(n) for n=0..98.

Formula

pi/(2*A199460)

Example

0.828700120129003061896869

Mathematica

digits = 99; Pi/(2 FindRoot[x == 2*Sin[x], {x, 2}, WorkingPrecision -> digits+1] [[1, 2]]) // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 20 2014 *)

Crossrefs

Cf. A199460, A211268.

Sequence in context: A246849 A143531 A352473 * A278809 A306617 A278261

Adjacent sequences: A211266 A211267 A211268 * A211270 A211271 A211272

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Apr 07 2012

Status

approved