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A224273
Decimal expansion of Baxter's four-coloring constant.
3
1, 4, 6, 0, 9, 9, 8, 4, 8, 6, 2, 0, 6, 3, 1, 8, 3, 5, 8, 1, 5, 8, 8, 7, 3, 1, 1, 7, 8, 4, 6, 0, 5, 9, 6, 9, 7, 0, 3, 8, 9, 3, 1, 3, 5, 5, 8, 0, 7, 4, 6, 1, 7, 8, 8, 2, 0, 5, 7, 7, 5, 4, 3, 4, 4, 4, 1, 5, 2, 1, 3, 5, 5, 8, 8, 5, 7, 3, 1, 4, 4, 0, 7, 7, 6, 5, 3
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
R. J. Baxter, Colorings of a hexagonal lattice, Journal of Mathematical Physics, Vol. 11, No. 3 (1970), pp. 784-789.
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