A036792 Decimal expansion of Integral_{x=0..Pi} (sin(x)/x) dx.

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

Offset

1,2

Comments

Also known as Gibbs constant.

Integral(sin(x)/x dx) = x - x^3/(3*3!) + x^5/(5*5!) - x^7/(7*7!) + ... - Harry J. Smith, May 01 2009

Also called Wilbraham-Gibbs (or Gibbs-Wilbraham) constant after the English mathematician Henry Wilbraham (1825-1883) and the American scientist Josiah Willard Gibbs (1839-1903). - Amiram Eldar, Jun 15 2021

This constant and its negative are respectively the maximum and the minimum value of Integral_{0..x} (sin(t)/t) dt for real x. - Jianing Song, Mar 10 2023

References

Steven Finch, Mathematical Constants, Cambridge University Press, 2003, section 4.1, "Gibbs-Wilbraham Constant", pp. 248-250.

Links

Harry J. Smith, Table of n, a(n) for n = 1..20000

J. Willard Gibbs, Fourier's Series, Nature, Vol. 59, No. 1539 (1899), p. 606.

Simon Plouffe, Gibbs, Si(Pi) or the Gibbs Constant to 1024 places.

Eric Weisstein's World of Mathematics, Wilbraham-Gibbs Constant.

Henry Wilbraham, On a certain periodic function, The Cambridge and Dublin Mathematical Journal, Vol. 3 (1848), pp. 198-201.

Example

1.85193705198246617036105337015799136334580972898115...

Mathematica

RealDigits[ N[ SinIntegral[Pi], 110]] [[1]]

Prog

(PARI) { default(realprecision, 20080); y=0; x=Pi; m=x; x2=x*x; n=1; nf=1; s=1; while (x!=y, y=x; n++; nf*=n; n++; nf*=n; m*=x2; s=-s; x+=s*m/(n*nf)); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b036792.txt", n, " ", d)); } \\ Harry J. Smith, May 01 2009

Crossrefs

Cf. A036790.

Sequence in context: A307384 A261882 A021058 * A334497 A335932 A198581

Adjacent sequences: A036789 A036790 A036791 * A036793 A036794 A036795

Keyword

nonn,cons

Author

N. J. A. Sloane

Status

approved