A061444 Decimal expansion of log(2 * Pi).

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

Offset: 1

Author

Frank Ellermann, Jun 11 2001

Keywords

• nonn
• cons

Comments

Used in formulas for gamma(x), e.g., in Stirling's approximation for m!.

Also decimal expansion of zeta'(0)/zeta(0). - Benoit Cloitre, Sep 28 2002

The value of log(2*Pi) is close to 1 + Sum_{n>=2} log(zeta(n)) = 1.83067035427178011248.... - Arkadiusz Wesolowski, Jul 17 2011

Examples

			1.837877066409345483560659472811235279722794947275566825634303...
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Simon Plouffe, log(2*Pi) to 10000 digits
• Simon Plouffe, Log(2*pi) to 2000 places

Crossrefs

Cf. A002162, A053510, A094642, A131659.

Programs

Mathematica

RealDigits[N[Log[2*Pi], 100]][[1]] (* Arkadiusz Wesolowski, Aug 29 2011 *)

PARI

{ default(realprecision, 20080); x=log(2*Pi); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b061444.txt", n, " ", d)) } \\ Harry J. Smith, Jul 22 2009

Formula

Equals A002162 + A053510 = A131659 - A094642. - R. J. Mathar, Aug 27 2011

Equals 1 + Sum_{k>=1} zeta(2*k)/(k*(2*k + 1)). - Amiram Eldar, Aug 20 2020