OFFSET
0,2
COMMENTS
Named after Richard Roxby Hall and Hugh Lowell Montgomery. - Amiram Eldar, Aug 25 2020
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 205-207.
LINKS
Andrew Granville and Kannan Soundararajan, The spectrum of multiplicative functions, Annals of Mathematics, Vol. 153, No. 2 (2001), pp. 407-470.
R. R. Hall, Proof of a conjecture of Heath-Brown concerning quadratic residues, Proceedings of the Edinburgh Mathematical Society, Vol. 39, No. 3 (1996), pp. 581-588.
Terence Tao, On product representations of squares, arXiv:2405.11610 [math.NT], May 2024. See page 2, (1.2).
Eric Weisstein's World of Mathematics, Hall-Montgomery Constant.
FORMULA
Equals 1 + Pi^2/6 + 2*PolyLog(2, -sqrt(e)).
Equals (1 - A126689)/2. - Amiram Eldar, Aug 25 2020
Equals 1 - A246849. - Hugo Pfoertner, May 25 2024
EXAMPLE
0.17150049314153606586...
MATHEMATICA
RealDigits[1+Pi^2/6+2PolyLog[2, -Sqrt[E]], 10, 120][[1]] (* Harvey P. Dale, Jul 18 2013 *)
PROG
(Python)
from mpmath import mp, pi, e, polylog, sqrt
mp.dps=106
print([int(z) for z in list(str(1 + pi**2/6 + 2* polylog(2, - sqrt(e)))[2:-1])]) # Indranil Ghosh, Jul 04 2017
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Aug 05 2008
STATUS
approved