A122914 Decimal expansion of (1 + log(2*Pi))/2, the entropy of the standard normal distribution.

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

Offset: 1

Author

Joseph Biberstine (jrbibers(AT)indiana.edu), Sep 18 2006

Keywords

• cons
• easy
• nonn

Comments

For a normal distribution with standard deviation sigma, add log(sigma). - Stanislav Sykora, Jan 15 2017

Examples

			1.4189385332046727417803297364056176398613974736377834128171515404827656959...
		

Links

• Wikipedia, Normal distribution.

Crossrefs

Partial quotients in A122915.

Cf. A061444, A075700.

Programs

Mathematica

RealDigits[(1 + Log[2 Pi])/2, 10, 80]

Formula

Equals (1 + log(2*Pi))/2 = 1/2 - A075700 = (1 + A061444)/2.

Equals -zeta(0) - zeta'(0). - Peter Luschny, May 16 2020

Equals 1 + G'(1), where G(x) is the Barnes G-function. - Amiram Eldar, Jun 08 2022

Extensions

a(80) corrected by Georg Fischer, Jul 10 2021