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

0,2

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.

Formula

Equals Sum_{k>=1} (1/sqrt(2*Pi*k) - k^k/(k!*exp(k))). - Amiram Eldar, Oct 13 2020

Example

0.0840695087...

Mathematica

Flatten[{0, RealDigits[2/3 + Zeta[1/2]/Sqrt[2*Pi], 10, 100][[1]]}] (* Vaclav Kotesovec, Aug 16 2015 *)

Prog

(PARI) 2/3 + zeta(1/2)/sqrt(2*Pi) \\ Michel Marcus, Aug 15 2015

Crossrefs

Cf. A019727, A059750, A231863.

Sequence in context: A364945 A354632 A114313 * A151558 A103613 A104768

Adjacent sequences: A096613 A096614 A096615 * A096617 A096618 A096619

Keyword

nonn,cons

Author

Eric W. Weisstein, Jun 30 2004

Status

approved