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A244920
Decimal expansion of 2*log(1+sqrt(2)), the integral over the square [0,1]x[0,1] of 1/sqrt(x^2+y^2) dx dy.
14
1, 7, 6, 2, 7, 4, 7, 1, 7, 4, 0, 3, 9, 0, 8, 6, 0, 5, 0, 4, 6, 5, 2, 1, 8, 6, 4, 9, 9, 5, 9, 5, 8, 4, 6, 1, 8, 0, 5, 6, 3, 2, 0, 6, 5, 6, 5, 2, 3, 2, 7, 0, 8, 2, 1, 5, 0, 6, 5, 9, 1, 2, 1, 7, 3, 0, 6, 7, 5, 4, 3, 6, 8, 4, 4, 4, 0, 5, 2, 1, 7, 5, 6, 6, 7, 4, 1, 3, 7, 8, 3, 8, 2, 0, 5, 1, 2, 0, 8, 5, 7
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
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
Equals twice A091648. - Michel Marcus, Mar 18 2017
Cf. A156035.
Sequence in context: A068469 A276459 A181152 * A073011 A086312 A370746
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved