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A036792
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Decimal expansion of Integral_{x=0..Pi} (sin(x)/x) dx.
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8
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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
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OFFSET
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1,2
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COMMENTS
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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
This constant and its negative are respectively the maximum and the minimum value of Integral_{0..x} (sin(t)/t) dt for real x. - Jianing Song, Mar 10 2023
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REFERENCES
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Steven Finch, Mathematical Constants, Cambridge University Press, 2003, section 4.1, "Gibbs-Wilbraham Constant", pp. 248-250.
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LINKS
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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.
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EXAMPLE
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1.85193705198246617036105337015799136334580972898115...
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MATHEMATICA
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RealDigits[ N[ SinIntegral[Pi], 110]] [[1]]
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PROG
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(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
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CROSSREFS
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Cf. A036790.
Sequence in context: A307384 A261882 A021058 * A334497 A335932 A198581
Adjacent sequences: A036789 A036790 A036791 * A036793 A036794 A036795
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KEYWORD
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nonn,cons
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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