OFFSET
1,2
COMMENTS
Number field regulator of the cyclotomic number field Q(zeta_8), where zeta_8 = sqrt(i), an eighth root of 1. - Alonso del Arte, Mar 11 2017
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
D. H. Bailey, J. M. Borwein and R. E. Crandall, Advances in the theory of box integrals, Math. Comp., Vol. 79, No. 271 (2010), pp. 1839-1866. See p. 1860.
FORMULA
Equals 2*arcsinh(1).
Equals Integral_{x>=1} 1/(x*(1+x)^(1/2)) dx. - Pointed out by Robert FERREOL.
Equals arccosh(3). - Vaclav Kotesovec, Dec 11 2016
Equals Integral_{x>=1} arcsinh(x)/x^2 dx. - Amiram Eldar, Jun 26 2021
Equals Integral_{x = 0..Pi/2} x/cos(x/2) dx. - Peter Bala, Aug 13 2024
Equals log(A156035). - Hugo Pfoertner, Aug 17 2024
EXAMPLE
1.7627471740390860504652186499595846180563206565232708215065912173...
MATHEMATICA
RealDigits[2 * Log[1 + Sqrt[2]], 10, 101] // First
RealDigits[NumberFieldRegulator[Sqrt[I]], 10, 100][[1]] (* Alonso del Arte, Mar 11 2017 *)
PROG
(PARI) 2*asinh(1) \\ Michel Marcus, Mar 18 2017
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Jul 08 2014
STATUS
approved