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%I #29 Aug 14 2020 11:23:15
%S 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,
%T 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,
%U 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
%N Decimal expansion of Soldner's constant.
%C From _Amiram Eldar_, Aug 14 2020: (Start)
%C The only positive solution to li(x) = 0, where li is the logarithmic integral.
%C Named after the German physicist, mathematician and astronomer Johann Georg von Soldner (1776 - 1833).
%C Also known as Ramanujan-Soldner constant.
%C Mascheroni (1792) calculated the value 1.45137. Soldner (1809) calculated the value 1.4513692346. (End)
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003. See p. 425.
%H Robert Price, <a href="/A070769/b070769.txt">Table of n, a(n) for n = 1..10000</a>
%H Bruce C. Berndt and Ronald J. Evans, <a href="https://doi.org/10.1016/0377-0427(91)90104-R">Some elegant approximations and asymptotic formulas of Ramanujan</a>, Journal of computational and applied mathematics, Vol. 37 No. 1-3 (1991), pp. 35-41. See p. 38.
%H Lorenzo Mascheroni, <a href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=1365785&search_terms=DTL4">Adnotationes ad calculum integralem Euleri, In quibus nonnulla Problemata ab Eulero proposita resolvuntur, Pars altera</a>, Petrus Galeatius, Ticini 1792. See p. 17.
%H Niels Nielsen, <a href="https://archive.org/details/diegammafunktion00niel">Die Gammafunktion</a>, New York : Chelsea, 1965.
%H Johann Georg von Soldner, <a href="https://archive.org/details/bub_gb_g4Q_AAAAcAAJ/page/n49/mode/2up">Théorie et tables d'une nouvelle fonction transcendante</a>, München: Lindauer, 1809. See p. 42.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SoldnersConstant.html">Soldner's Constant</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LogarithmicIntegral.html">Logarithmic Integral</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Logarithmic_integral_function">Logarithmic integral function</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Ramanujan%E2%80%93Soldner_constant">Ramanujan-Soldner constant</a>.
%H Marek Wolf, <a href="https://www.researchgate.net/publication/330413076_The_relations_between_Euler-Mascheroni_and_Ramanujan-Soldner_constants">The relations between Euler-Mascheroni and Ramanujan-Soldner constants</a>, 2019.
%F Equals exp(A091723). - _Amiram Eldar_, Aug 14 2020
%e 1.45136923488338105028396848589...
%t RealDigits[ x /. FindRoot[ LogIntegral[x] == 0, {x, 2}, WorkingPrecision -> 105]][[1]] (* _Jean-François Alcover_, Nov 08 2012 *)
%o (PARI) solve(x=1.4,2,real(eint1(-log(x)))) \\ _Charles R Greathouse IV_, Feb 23 2017
%Y Cf. A091723.
%K nonn,cons
%O 1,2
%A _Eric W. Weisstein_, May 05 2002
%E Offset corrected and example added by _Stanislav Sykora_, May 18 2012
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