A070769 Decimal expansion of Soldner's constant.
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
Examples
1.45136923488338105028396848589...
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.
Crossrefs
Cf. A091723.
Programs
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Mathematica
RealDigits[ x /. FindRoot[ LogIntegral[x] == 0, {x, 2}, WorkingPrecision -> 105]][[1]] (* Jean-François Alcover, Nov 08 2012 *) -
PARI
solve(x=1.4,2,real(eint1(-log(x)))) \\ Charles R Greathouse IV, Feb 23 2017
Formula
Equals exp(A091723). - Amiram Eldar, Aug 14 2020
Extensions
Offset corrected and example added by Stanislav Sykora, May 18 2012
Comments