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A070769
Decimal expansion of Soldner's constant.
15
1, 4, 5, 1, 3, 6, 9, 2, 3, 4, 8, 8, 3, 3, 8, 1, 0, 5, 0, 2, 8, 3, 9, 6, 8, 4, 8, 5, 8, 9, 2, 0, 2, 7, 4, 4, 9, 4, 9, 3, 0, 3, 2, 2, 8, 3, 6, 4, 8, 0, 1, 5, 8, 6, 3, 0, 9, 3, 0, 0, 4, 5, 5, 7, 6, 6, 2, 4, 2, 5, 5, 9, 5, 7, 5, 4, 5, 1, 7, 8, 3, 5, 6, 5, 9, 5, 3, 1, 3, 5, 7, 7, 1, 1, 0, 8, 6, 8, 2, 8, 8, 4
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
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.
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.
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
Cf. A091723.
Sequence in context: A016493 A101626 A195853 * A021693 A188944 A010662
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, May 05 2002
EXTENSIONS
Offset corrected and example added by Stanislav Sykora, May 18 2012
STATUS
approved