|
| |
|
|
A016634
|
|
Decimal expansion of log(11).
|
|
5
|
|
|
|
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, 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, 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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
REFERENCES
|
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.
|
|
|
LINKS
|
Milton Abramowitz and Irene A. Stegun, eds.,Handbook of Mathematical Functions,National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
|
|
|
FORMULA
|
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
Equals 2*(log 2+log 5 -log 3)+Sum_{k>=1} (-1)^k/(k*100^k). -R. J. Mathar,Jun 10 2024
|
|
|
EXAMPLE
|
2.3978952727983705440619435779651292998217068539374171752185677...
|
|
|
MATHEMATICA
|
|
|
|
PROG
|
(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
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
