A115287 - OEIS

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

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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