OFFSET
1,2
COMMENTS
From Amiram Eldar, Aug 14 2020: (Start)
The only positive solution to li(x) = 0, where li is the logarithmic integral.
Named after the German physicist, mathematician and astronomer Johann Georg von Soldner (1776 - 1833).
Also known as Ramanujan-Soldner constant.
Mascheroni (1792) calculated the value 1.45137. Soldner (1809) calculated the value 1.4513692346. (End)
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003. See p. 425.
LINKS
Robert Price, Table of n, a(n) for n = 1..10000
Bruce C. Berndt and Ronald J. Evans, Some elegant approximations and asymptotic formulas of Ramanujan, Journal of computational and applied mathematics, Vol. 37 No. 1-3 (1991), pp. 35-41. See p. 38.
Lorenzo Mascheroni, Adnotationes ad calculum integralem Euleri, In quibus nonnulla Problemata ab Eulero proposita resolvuntur, Pars altera, Petrus Galeatius, Ticini 1792. See p. 17.
Niels Nielsen, Die Gammafunktion, New York : Chelsea, 1965.
Johann Georg von Soldner, Théorie et tables d'une nouvelle fonction transcendante, München: Lindauer, 1809. See p. 42.
Eric Weisstein's World of Mathematics, Soldner's Constant.
Eric Weisstein's World of Mathematics, Logarithmic Integral.
Wikipedia, Logarithmic integral function.
Wikipedia, Ramanujan-Soldner constant.
Marek Wolf, The relations between Euler-Mascheroni and Ramanujan-Soldner constants, 2019.
FORMULA
Equals exp(A091723). - Amiram Eldar, Aug 14 2020
EXAMPLE
1.45136923488338105028396848589...
MATHEMATICA
RealDigits[ x /. FindRoot[ LogIntegral[x] == 0, {x, 2}, WorkingPrecision -> 105]][[1]] (* Jean-François Alcover, Nov 08 2012 *)
PROG
(PARI) solve(x=1.4, 2, real(eint1(-log(x)))) \\ Charles R Greathouse IV, Feb 23 2017
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, May 05 2002
EXTENSIONS
Offset corrected and example added by Stanislav Sykora, May 18 2012
STATUS
approved