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Decimal expansion of log(11).
5

%I #28 Jun 10 2024 07:44:38

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

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

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

%N Decimal expansion of log(11).

%D Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 2.

%H Harry J. Smith, <a href="/A016634/b016634.txt">Table of n, a(n) for n = 1..20000</a>

%H Milton Abramowitz and Irene A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F log(11) = 2*Sum_{n >= 1} 1/(n*P(n, 6/5)*P(n-1, 6/5)), where P(n, x) denotes the n-th Legendre polynomial. The first 20 terms of the series gives the approximation log(11) = 2.3978952727(47...), correct to 10 decimal places. - _Peter Bala_, Mar 19 2024

%F Equals 2*(log 2+log 5 -log 3)+Sum_{k>=1} (-1)^k/(k*100^k). - _R. J. Mathar_, Jun 10 2024

%e 2.3978952727983705440619435779651292998217068539374171752185677...

%t RealDigits[Log[11], 10, 120][[1]] (* _Harvey P. Dale_, Mar 09 2014 *)

%o (PARI) default(realprecision, 20080); x=log(11); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016634.txt", n, " ", d)); \\ _Harry J. Smith_, May 16 2009

%Y Cf. A016739 Continued fraction.

%K nonn,cons

%O 1,1

%A _N. J. A. Sloane_