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.

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

Author

Jean-François Alcover, Jul 08 2014

Keywords

• nonn
• cons
• easy

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

Examples

			1.7627471740390860504652186499595846180563206565232708215065912173...
		

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.
• LMFDB, Global Number Field 4.0.256.1: Q(zeta_8).
• Index entries for transcendental numbers

Crossrefs

Equals twice A091648. - Michel Marcus, Mar 18 2017

Cf. A156035.

Programs

Mathematica

RealDigits[2 * Log[1 + Sqrt[2]], 10, 101] // First
RealDigits[NumberFieldRegulator[Sqrt[I]], 10, 100][[1]] (* Alonso del Arte, Mar 11 2017 *)

PARI

2*asinh(1) \\ Michel Marcus, Mar 18 2017

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

Equals arcsinh(2*sqrt(2)). - Akiva Weinberger, Dec 03 2024

Equals Integral_{x=0..oo} erf(sqrt(x))/(x*e^x) dx. - Kritsada Moomuang, May 25 2025