OFFSET
1,1
COMMENTS
By the Lindemann-Weierstrass theorem, this constant is transcendental. - Charles R Greathouse IV, May 14 2019
FORMULA
Equals (exp(1)+1)/(exp(1)-1).
Equals (BesselI(3/2,1/2)/BesselI(1/2,1/2))+2.
Equals BesselI(-1/2,1/2)/BesselI(1/2,1/2).
Equals 2 * Sum_{k>=0} B(2*k)/(2*k)!, where B(2*k) = A000367(k)/A002445(k) are the Bernoulli numbers. - Amiram Eldar, Nov 25 2020
Equals 2 * A073333 + 1. - Antonio GraciĆ” Llorente, Jan 21 2024
EXAMPLE
2.163953413738... = 2 + 1/(6 + 1/(10 + 1/(14 + 1/(18 + ...)))).
MATHEMATICA
RealDigits[Coth[1/2], 10, 120][[1]] (* or *) BesselI[-1/2, 1/2]/BesselI[1/2, 1/2]
PROG
(PARI) cotanh(1/2) \\ Michel Marcus, Mar 28 2019
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Terry D. Grant, Mar 27 2019
STATUS
approved