OFFSET
1,2
REFERENCES
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.
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..20000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Matt Parker, What's the story with log(1 + 2 + 3)?, standupmaths video (2019)
FORMULA
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
EXAMPLE
1.791759469228055000812477358380702272722990692183004705855374343130887...
MATHEMATICA
First[RealDigits[Log[6], 10, 100]] (* Paolo Xausa, Mar 21 2024 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved