A036793 Decimal expansion of (2/Pi)*Integral_{x=0..Pi} sin(x)/x dx.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Comments

Integral(sin(x)/x dx) = x - x^3/(3*3!) + x^5/(5*5!) - x^7/(7*7!) + ... . - Harry J. Smith, Apr 28 2009

Examples

			1.17897974447216727..., the constant in Gibbs phenomenon.
		

References

• E. J. Borowski and J. M. Borwein, Dictionary of Mathematics, 3rd printing, Harper Collins, 1991, Gibbs phenomenon.
• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.1 Gibbs-Wilbraham Constant, p. 249.

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Eric Weisstein's World of Mathematics, Wilbraham-Gibbs Constant

Crossrefs

Cf. A036791 (continued fraction), A061079 for Si( x ).

Programs

Mathematica

RealDigits[ N[ (2/Pi)*SinIntegral[Pi], 105]][[1]] (* Jean-François Alcover, Nov 07 2012 *)

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)); x*=2/Pi; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b036793.txt", n, " ", d)); } \\ Harry J. Smith, Apr 28 2009

Formula

A036792 divided by A019669. - R. J. Mathar, Mar 22 2011