A122915 -id:A122915

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A122914

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

+10
1

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..104.

Wikipedia, Normal distribution.

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

EXAMPLE

1.4189385332046727417803297364056176398613974736377834128171515404827656959...

MATHEMATICA

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

CROSSREFS

Partial quotients in A122915.

Cf. A061444, A075700.

KEYWORD

cons,easy,nonn

AUTHOR

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

EXTENSIONS

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

STATUS

approved

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