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A036793
Decimal expansion of (2/Pi)*Integral_{x=0..Pi} sin(x)/x dx.
6
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
1,3
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
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
KEYWORD
nonn,cons
STATUS
approved