|
|
A196530
|
|
Decimal expansion of log(2+sqrt(3))/sqrt(3).
|
|
6
|
|
|
7, 6, 0, 3, 4, 5, 9, 9, 6, 3, 0, 0, 9, 4, 6, 3, 4, 7, 5, 3, 1, 0, 9, 4, 2, 5, 4, 8, 8, 0, 4, 0, 5, 8, 2, 4, 2, 0, 1, 6, 2, 7, 7, 3, 0, 9, 4, 7, 1, 7, 6, 4, 2, 7, 0, 2, 0, 5, 7, 0, 6, 7, 0, 2, 6, 0, 0, 5, 5, 1, 2, 2, 6, 5, 4, 9, 1, 0, 7, 5, 3, 0, 2, 8, 4, 5, 8, 3, 6
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
Equals the value of the Dirichlet L-series of a non-principal character modulo 12 (A110161) at s=1.
|
|
REFERENCES
|
L. B. W. Jolley, Summation of series, Dover (1961), eq. (83), page 16.
|
|
LINKS
|
|
|
FORMULA
|
Equals Sum_{k>=1} (-1)^(k+1)*2^k/(k * binomial(2*k,k)). - Amiram Eldar, Aug 19 2020
Equals 1/Product_{p prime} (1 - Kronecker(12,p)/p), where Kronecker(12,p) = 0 if p = 2 or 3, 1 if p == 1 or 11 (mod 12) or -1 if p == 5 or 7 (mod 12). - Amiram Eldar, Dec 17 2023
Equals (1/2)*2F1(1/2,1;3/2;3/4) [Krupnikov] - R. J. Mathar, Jun 11 2024
|
|
EXAMPLE
|
0.7603459963009463475310942548...
|
|
MATHEMATICA
|
RealDigits[Log[2 + Sqrt[3]]/Sqrt[3], 10, 89][[1]] (* Bruno Berselli, Dec 20 2011 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|