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
G. C. Greubel, Table of n, a(n) for n = 1..10000
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
KEYWORD
AUTHOR
Clark Kimberling, Mar 01 2018
STATUS
approved