login
A299619
Decimal expansion of e^(W(1) + W(1/e)) = (1/e)/(W(1)*W(1/e)), where W is the Lambert W function (or PowerLog); see Comments.
4
2, 3, 2, 9, 3, 9, 3, 2, 6, 6, 8, 4, 2, 7, 9, 3, 2, 2, 4, 8, 5, 7, 6, 3, 0, 9, 1, 5, 6, 2, 7, 5, 2, 1, 9, 4, 3, 5, 7, 7, 4, 3, 9, 1, 9, 8, 0, 2, 3, 3, 3, 1, 5, 1, 3, 4, 6, 7, 1, 4, 9, 2, 5, 2, 4, 7, 2, 6, 0, 2, 7, 8, 6, 1, 6, 3, 1, 0, 9, 1, 0, 5, 1, 1, 6, 6
OFFSET
1,1
COMMENTS
The Lambert W function satisfies the functional equation e^(W(x) + W(y)) = x*y/(W(x)*W(y)) for x and y greater than -1/e, so that e^(W(1) + W(1/e)) = (1/e)/(W(1)*W(1/e)). See A299613 for a guide to related constants.
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function
EXAMPLE
e^(W(1) + W(1/e)) = 2.3293932668427932248576309...
MATHEMATICA
w[x_] := ProductLog[x]; x = 1; y = 1/E;
N[E^(w[x] + w[y]), 130] (* A299619 *)
RealDigits[1/(E*LambertW[1]*LambertW[1/E]), 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)
PROG
(PARI) exp(-1)/(lambertw(1)*lambertw(exp(-1))) \\ G. C. Greubel, Mar 03 2018
CROSSREFS
Sequence in context: A349972 A163204 A364895 * A215269 A352485 A356092
KEYWORD
nonn,cons,easy
AUTHOR
Clark Kimberling, Mar 01 2018
STATUS
approved