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 A036792 Decimal expansion of Integral_{x=0..Pi} sin(x)/x. 8
 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 (list; constant; graph; refs; listen; history; text; internal format)
 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 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 STATUS approved

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Last modified February 6 04:21 EST 2023. Contains 360097 sequences. (Running on oeis4.)