OFFSET
1,2
COMMENTS
The constant is named after Australian physicist Rodney James Baxter. - Amiram Eldar, Aug 13 2020
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003. See p. 413.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..5000
R. J. Baxter, Colorings of a hexagonal lattice, Journal of Mathematical Physics, Vol. 11, No. 3 (1970), pp. 784-789.
R. J. Baxter, q colourings of the triangular lattice, Journal of Physics A: Mathematical and General, Vol. 19, No. 14 (1986), pp. 2821-2839.
Eric Weisstein's World of Mathematics, Baxter's Four-Coloring Constant.
FORMULA
Equals 1/Product_{n>=1} (1-1/(3n-1)^2) = 3*Gamma(1/3)^3/(4*Pi^2).
Equals 1/(2^(1/3)*A081760). - Kritsada Moomuang, Mar 15 2020
Equals 2*Pi/(sqrt(3)*Gamma(2/3)^3). - Vaclav Kotesovec, Mar 23 2020
Equals Product_{k>=1} (1 + 1/A152751(k)). - Amiram Eldar, Aug 13 2020
Equals Sum_{k>=0} binomial(-1/3, k)^2. - Gerry Martens, Jul 24 2023
EXAMPLE
1.46099848620631835815887311784605969703893135580746178820577543...
MATHEMATICA
RealDigits[3 Gamma[1/3]^3/(4 Pi^2), 10, 90][[1]]
PROG
(PARI) 3*gamma(1/3)^3/(4*Pi^2) \\ Michel Marcus, Mar 23 2020
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Bruno Berselli, Apr 02 2013
STATUS
approved