A070769 - OEIS

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

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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...