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Decimal expansion of log(2 * Pi).
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%I #32 Aug 20 2020 08:31:49

%S 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,

%T 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,

%U 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

%N Decimal expansion of log(2 * Pi).

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

%C Also decimal expansion of zeta'(0)/zeta(0). - _Benoit Cloitre_, Sep 28 2002

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

%H Harry J. Smith, <a href="/A061444/b061444.txt">Table of n, a(n) for n = 1..20000</a>

%H Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/log2pi.txt">log(2*Pi) to 10000 digits</a>

%H Simon Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap60.html">Log(2*pi) to 2000 places</a>

%F Equals A002162 + A053510 = A131659 - A094642. - _R. J. Mathar_, Aug 27 2011

%F Equals 1 + Sum_{k>=1} zeta(2*k)/(k*(2*k + 1)). - _Amiram Eldar_, Aug 20 2020

%e 1.837877066409345483560659472811235279722794947275566825634303...

%t RealDigits[N[Log[2*Pi], 100]][[1]] (* _Arkadiusz Wesolowski_, Aug 29 2011 *)

%o (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

%Y Cf. A002162, A053510, A094642, A131659.

%K nonn,cons

%O 1,2

%A _Frank Ellermann_, Jun 11 2001