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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. 11
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 (list; constant; graph; refs; listen; history; text; internal format)
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, R. E. Crandall, Advances in the theory of box integrals (2010) p. 22.

LMFDB, Global Number Field 4.0.256.1: Q(zeta_8).

Index entries for transcendental numbers

FORMULA

Also equals 2*arcsinh(1).

Also equals Integral_{1..infinity} 1/(x*(1+x)^(1/2)) dx. - Pointed out by Robert FERREOL.

Equals arccosh(3). - Vaclav Kotesovec, Dec 11 2016

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

Sequence in context: A068469 A276459 A181152 * A073011 A086312 A214280

Adjacent sequences:  A244917 A244918 A244919 * A244921 A244922 A244923

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Jul 08 2014

STATUS

approved

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Last modified May 12 12:47 EDT 2021. Contains 343823 sequences. (Running on oeis4.)