A036793 - OEIS

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,3

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

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

FORMULA

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

EXAMPLE

1.17897974447216727..., the constant in Gibbs phenomenon.

MATHEMATICA

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

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)); 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

CROSSREFS

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

Sequence in context: A257237 A242022 A085676 * A257394 A196278 A006969

Adjacent sequences: A036790 A036791 A036792 * A036794 A036795 A036796

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane

STATUS

approved