A094936 Decimal expansion of 2/(Pi*e).

2, 3, 4, 1, 9, 9, 3, 2, 6, 0, 9, 7, 2, 7, 6, 6, 4, 2, 7, 6, 0, 9, 6, 9, 0, 7, 3, 8, 6, 6, 6, 6, 7, 4, 8, 8, 8, 5, 5, 6, 5, 9, 6, 8, 5, 1, 0, 4, 2, 4, 5, 7, 9, 5, 5, 0, 7, 8, 8, 9, 0, 4, 3, 8, 8, 0, 6, 5, 1, 3, 8, 7, 0, 7, 4, 8, 7, 8, 2, 6, 1, 5, 3, 2, 0, 7, 5, 0, 4, 4, 0, 3, 6, 2, 3, 3, 4, 5, 7, 2, 6, 2, 6, 2

Offset: 0

Author

Benoit Cloitre, Jun 18 2004

Keywords

• cons
• nonn

Comments

If N(n) denotes the number of real roots of the n-th Bernoulli polynomial then lim_{n->oo} N(n)/n = 2/(e*Pi).

Examples

			0.23419932609727664276...
		

Links

• A. P. Veselov and J.P. Ward, On the real roots of the Bernoulli polynomials and the Hurwitz zeta-function, 1999.
• A. P. Veselov and J.P. Ward, On the real zeroes of the Hurwitz zeta-function and Bernoulli polynomials, J. Math. Anal. Appl. 305 (2) (2005) 712-721.

Crossrefs

Cf. A000796 (Pi), A001113 (e), A019609, A019610.

Programs

Mathematica

RealDigits[2/(Pi*E), 10, 120][[1]] (* Amiram Eldar, Apr 28 2025 *)

PARI

2/exp(1)/Pi \\ Charles R Greathouse IV, Jan 14 2017

Formula

Equals 1/A019610. - Michel Marcus, Dec 07 2013