A115287 Decimal expansion of 1/(1+LambertW(1)).

6, 3, 8, 1, 0, 3, 7, 4, 3, 3, 6, 5, 1, 1, 0, 7, 7, 8, 5, 2, 2, 4, 0, 7, 3, 8, 5, 5, 1, 9, 8, 8, 0, 3, 1, 4, 4, 4, 3, 9, 3, 3, 8, 4, 1, 2, 8, 9, 0, 2, 7, 6, 4, 0, 4, 1, 9, 4, 8, 3, 1, 9, 3, 6, 5, 0, 3, 4, 2, 1, 0, 1, 0, 5, 6, 7, 6, 0, 0, 8, 3, 0, 4, 1, 0, 0, 1, 8, 5, 2, 5, 1, 0, 5, 2, 7, 4, 8, 3, 3, 1, 5, 7, 0, 9

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Cristina B. Corcino, Roberto B. Corcino and István Mező, Continued fraction expansions for the Lambert W function, Aequationes mathematicae, Vol. 93, No. 2 (2019), pp. 485-49.

Mathematics Stack Exchange, Interesting integral related to the Omega Constant/Lambert W Function, 2011.

Victor H. Moll, Some Questions in the Evaluation of Definite Integrals, MAA Short Course, San Antonio, TX, January 2006.

Eric Weisstein's World of Mathematics, Omega Constant.

Eric Weisstein's World of Mathematics, Definite Integral.

Formula

Equals Integral_{x=-oo..oo} 1/(Pi^2 + (exp(x)-x)^2) dx (discovered by Victor Adamchik). - Amiram Eldar, Jul 04 2021

Example

0.63810374336511077852...

Mathematica

RealDigits[1/(1 + ProductLog[1]), 10, 105] // First (* Jean-François Alcover, Feb 07 2013 *)

Prog

(PARI) 1/(1 + lambertw(1)) \\ G. C. Greubel, Nov 05 2017

Crossrefs

Cf. A006153, A030178, A097172, A097173, A097174, A265953, A276231, A302399.

Sequence in context: A371376 A096253 A182566 * A061533 A317969 A281682

Adjacent sequences: A115284 A115285 A115286 * A115288 A115289 A115290

Keyword

nonn,cons,easy

Author

Eric W. Weisstein, Jan 19 2006

Status

approved