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%I #30 Sep 12 2022 04:22:04
%S 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,
%T 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,
%U 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
%N Decimal expansion of (2/Pi)*Integral_{x=0..Pi} sin(x)/x dx.
%C Integral(sin(x)/x dx) = x - x^3/(3*3!) + x^5/(5*5!) - x^7/(7*7!) + ... . - _Harry J. Smith_, Apr 28 2009
%D E. J. Borowski and J. M. Borwein, Dictionary of Mathematics, 3rd printing, Harper Collins, 1991, Gibbs phenomenon.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.1 Gibbs-Wilbraham Constant, p. 249.
%H Harry J. Smith, <a href="/A036793/b036793.txt">Table of n, a(n) for n = 1..20000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Wilbraham-GibbsConstant.html">Wilbraham-Gibbs Constant</a>
%F A036792 divided by A019669. - _R. J. Mathar_, Mar 22 2011
%e 1.17897974447216727..., the constant in Gibbs phenomenon.
%t RealDigits[ N[ (2/Pi)*SinIntegral[Pi], 105]][[1]] (* _Jean-François Alcover_, Nov 07 2012 *)
%o (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
%Y Cf. A036791 (continued fraction), A061079 for Si( x ).
%K nonn,cons
%O 1,3
%A _N. J. A. Sloane_
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