|
%I #29 Mar 21 2024 16:11:04
%S 1,7,9,1,7,5,9,4,6,9,2,2,8,0,5,5,0,0,0,8,1,2,4,7,7,3,5,8,3,8,0,7,0,2,
%T 2,7,2,7,2,2,9,9,0,6,9,2,1,8,3,0,0,4,7,0,5,8,5,5,3,7,4,3,4,3,1,3,0,8,
%U 8,7,9,1,5,1,8,8,3,0,3,6,8,2,4,7,9,4,7,9,0,8,1,8,1,0,1,5,0,7,7
%N Decimal expansion of log(6).
%D M. Abramowitz and I. 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="/A016629/b016629.txt">Table of n, a(n) for n = 1..20000</a>
%H M. Abramowitz and I. 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 Matt Parker, <a href="https://www.youtube.com/watch?v=OcTMBrUutfk">What's the story with log(1 + 2 + 3)?</a>, standupmaths video (2019)
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F log(6) = 2*Sum_{n >= 1} 1/(n*P(n, 7/5)*P(n-1, 7/5)), where P(n, x) denotes the n-th Legendre polynomial. The first 20 terms of the series gives the approximation log(6) = 1.79175946922805(27...), correct to 14 decimal places. - _Peter Bala_, Mar 19 2024
%e 1.791759469228055000812477358380702272722990692183004705855374343130887...
%t First[RealDigits[Log[6], 10, 100]] (* _Paolo Xausa_, Mar 21 2024 *)
%o (PARI) default(realprecision, 20080); x=log(6); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016629.txt", n, " ", d)); \\ _Harry J. Smith_, May 16 2009
%Y Cf. A016734 (continued fraction).
%K nonn,cons
%O 1,2
%A _N. J. A. Sloane_
|
