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
Examples
0.63810374336511077852...
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.
Programs
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Mathematica
RealDigits[1/(1 + ProductLog[1]), 10, 105] // First (* Jean-François Alcover, Feb 07 2013 *)
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PARI
1/(1 + lambertw(1)) \\ G. C. Greubel, Nov 05 2017
Formula
Equals Integral_{x=-oo..oo} 1/(Pi^2 + (exp(x)-x)^2) dx (discovered by Victor Adamchik). - Amiram Eldar, Jul 04 2021