OFFSET
0,1
COMMENTS
The Lambert W function satisfies the functional equations
W(x) + W(y) = W(x*y(1/W(x) + 1/W(y)) = log(x*y)/(W(x)*W(y)) for x and y greater than -1/e, so that 2*W(1/3) = W(2)/(9*W(1/3)) = -2*log(3) - 2*log(W(1/3)). See A299613 for a guide to related sequences.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Lambert W-Function
EXAMPLE
2*W(1/3) = 0.5152553060994734085658324032521955...
MATHEMATICA
w[x_] := ProductLog[x]; x = 1/3; y = 1/3; u = N[w[x] + w[y], 100]
RealDigits[u, 10][[1]] (* A299628 *)
RealDigits[2*LambertW[1/3], 10, 100][[1]] (* G. C. Greubel, Mar 06 2018 *)
PROG
(PARI) 2*lambertw(1/3) \\ G. C. Greubel, Mar 06 2018
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Mar 03 2018
STATUS
approved