A096616 Decimal expansion of 2/3 + zeta(1/2)/sqrt(2*Pi).
0, 8, 4, 0, 6, 9, 5, 0, 8, 7, 2, 7, 6, 5, 5, 9, 9, 6, 4, 6, 1, 4, 8, 9, 5, 0, 2, 4, 7, 9, 0, 3, 5, 5, 1, 1, 9, 3, 7, 5, 7, 2, 7, 9, 6, 4, 6, 8, 0, 1, 1, 9, 6, 1, 8, 4, 2, 9, 7, 2, 7, 2, 4, 6, 0, 0, 1, 3, 5, 9, 7, 9, 0, 7, 0, 1, 6, 7, 7, 2, 0, 6, 2, 4, 8, 7, 4, 7, 5, 9, 8, 3, 1, 8, 9, 0, 6, 3, 6, 0, 9, 8
Offset: 0
Examples
0.0840695087...
References
- David H. Bailey, Jonathan M. Borwein, Neil J. Calkin, Roland Girgensohn, D. Russell Luke and Victor H. Moll, Experimental Mathematics in Action, Wellesley, MA: A K Peters, 2007, pp. 18 and 227.
- Jonathan Borwein, David Bailey and Roland Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery, Wellesley, MA: A K Peters, 2004, pp. 15-17.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..10000
- Jonathan M. Borwein and Scott B. Lindstrom, Meetings with Lambert W and other special functions in optimization and analysis, Pure and Applied Functional Analysis, Vol. 1, No. 3 (2016), pp. 361-396, alternative link.
- Donald E. Knuth, Problem 10832, The American Mathematical Monthly, Vol. 107, No. 9 (2000), p. 863, A Stirling Series, solution by Cecil C. Rousseau, ibid., Vol. 108, No. 9 (2001), pp. 877-878.
- Allen Stenger, Experimental Math for Math Monthly Problems, The American Mathematical Monthly, Vol. 124, No. 2 (2017), pp. 116-131, alternative link.
- Eric Weisstein's World of Mathematics, Knuth's Series.
Programs
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Mathematica
Flatten[{0, RealDigits[2/3 + Zeta[1/2]/Sqrt[2*Pi], 10, 100][[1]]}] (* Vaclav Kotesovec, Aug 16 2015 *) -
PARI
2/3 + zeta(1/2)/sqrt(2*Pi) \\ Michel Marcus, Aug 15 2015
Formula
Equals Sum_{k>=1} (1/sqrt(2*Pi*k) - k^k/(k!*exp(k))). - Amiram Eldar, Oct 13 2020
Equals 2/3 - A134469. - R. J. Mathar, Dec 17 2024