|
%I #31 Mar 21 2024 16:10:18
%S 2,1,9,7,2,2,4,5,7,7,3,3,6,2,1,9,3,8,2,7,9,0,4,9,0,4,7,3,8,4,5,0,5,1,
%T 4,0,9,2,9,4,9,8,1,1,1,5,6,4,5,4,9,8,9,0,3,4,6,9,3,8,8,6,6,7,2,7,4,9,
%U 8,8,5,8,6,4,3,7,2,1,7,9,3,3,7,4,7,2,3,1,5,0,9,6,2,7,4,6,4,1,7
%N Decimal expansion of log(9).
%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="/A016632/b016632.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 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F log(9) = 2*Sum_{n >= 1} 1/(n*P(n, 5/4)*P(n-1, 5/4)), where P(n, x) denotes the n-th Legendre polynomial. The first 20 terms of the series gives the approximation log(9) = 2.19722457733(34...), correct to 11 decimal places. - _Peter Bala_, Mar 18 2024
%e 2.197224577336219382790490473845051409294981115645498903469388667274988...
%t First[RealDigits[Log[9], 10, 100]] (* _Paolo Xausa_, Mar 21 2024 *)
%o (PARI) default(realprecision, 20080); x=log(9); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016632.txt", n, " ", d)); \\ _Harry J. Smith_, May 16 2009
%Y Cf. A016737 Continued fraction.
%K nonn,cons
%O 1,1
%A _N. J. A. Sloane_
|
