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%I #39 Feb 26 2024 16:19:50
%S 7,4,7,5,9,7,9,2,0,2,5,3,4,1,1,4,3,5,1,7,8,7,3,0,9,4,3,8,3,0,1,7,8,1,
%T 7,3,0,2,4,7,8,6,2,6,4,0,7,4,2,2,8,3,7,6,6,0,4,2,2,9,1,6,3,4,2,5,1,6,
%U 7,8,8,1,6,0,2,9,5,4,4,0,4,3,1,2,4,3,0,8,5,0,3,6,9,3,1,4,1,1,1,1,5
%N Decimal expansion of Rényi's parking constant.
%C Named after the Hungarian mathematician Alfréd Rényi (1921-1970). - _Amiram Eldar_, Jun 24 2021
%D A. Rényi, On a one-dimensional problem concerning random space-filling, Publ. Math. Inst. Hung. Acad. Sci., Vol. 3 (1958), pp. 109-127.
%H George Marsaglia, Arif Zaman and John C. W. Marsaglia, <a href="https://doi.org/10.1090/S0025-5718-1989-0969490-3">Numerical solution of some classical differential-difference equations</a>, Math. Comp., Vol. 53, No. 187 (1989), pp. 191-201.
%H Simon Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap71.html">The Parking or Renyi constant</a>. [broken link]
%H Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/parking.txt">The Parking or Renyi constant</a>.
%H Antonín Slavík, <a href="https://www2.karlin.mff.cuni.cz/~slavik/papers/parking-constant.pdf">De Bruijn's Short Route to Rényi's Parking Constant</a>, Univ. Karlova (Czechia, 2014). See p. 11.
%H Philipp O. Tsvetkov, <a href="https://doi.org/10.1038/s41598-020-77896-0">Stoichiometry of irreversible ligand binding to a one-dimensional lattice</a>, Scientific Reports, Springer Nature, Vol. 10 (2020), Article number: 21308.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RenyisParkingConstants.html">Rényi's Parking Constants</a>.
%F Equals exp(-2*gamma) * Integral_{x>=0} exp(2*Ei(-x))/x^2 dx, where gamma is Euler's constant (A001620) and Ei(x) is the exponential integral. - _Amiram Eldar_, Jun 24 2021
%e 0.7475979202534114351787309438301781730247862640742283766042291634251678816...
%t digits = 101; c = NIntegrate[E^(-2*(EulerGamma + Gamma[0, t] + Log[t])), {t, 0, Infinity}, WorkingPrecision -> digits + 10, MaxRecursion -> 20]; RealDigits[c, 10, digits][[1]] (* _Jean-François Alcover_, Nov 05 2012, updated May 21 2016 *)
%Y Cf. A001620, A050994, A050995.
%K nonn,cons
%O 0,1
%A _Eric W. Weisstein_
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