A016634 Decimal expansion of log(11).

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Examples

			2.3978952727983705440619435779651292998217068539374171752185677...
		

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

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• 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].
• Index entries for transcendental numbers

Crossrefs

Cf. A016739 Continued fraction.

Programs

Mathematica

RealDigits[Log[11], 10, 120][[1]] (* Harvey P. Dale, Mar 09 2014 *)

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

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