A050996 Decimal expansion of Rényi's parking constant.
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, 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, 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
Offset: 0
Examples
0.7475979202534114351787309438301781730247862640742283766042291634251678816...
References
- Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 5.3, p. 278.
- A. Rényi, On a one-dimensional problem concerning random space-filling, Publ. Math. Inst. Hung. Acad. Sci., Vol. 3 (1958), pp. 109-127.
Links
- George Marsaglia, Arif Zaman and John C. W. Marsaglia, Numerical solution of some classical differential-difference equations, Math. Comp., Vol. 53, No. 187 (1989), pp. 191-201.
- Simon Plouffe, The Parking or Renyi constant. [broken link]
- Simon Plouffe, The Parking or Renyi constant.
- Antonín Slavík, De Bruijn's Short Route to Rényi's Parking Constant, Amer. Math. Monthly 131 (2024), pp. 831-841 (preprint).
- Philipp O. Tsvetkov, Stoichiometry of irreversible ligand binding to a one-dimensional lattice, Scientific Reports, Springer Nature, Vol. 10 (2020), Article number: 21308.
- Eric Weisstein's World of Mathematics, Rényi's Parking Constants.
Programs
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Mathematica
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 *)
Formula
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
Comments