OFFSET
1,2
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 W(1) + W(3) = W(W(3/W(1)) + 3/W(3)) = log(3) - log(W(1)) - log(W(3)). See A299613 for a guide to related sequences.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Lambert W-Function
EXAMPLE
W(1) + W(3) = 1.6170521853738238329886657327632...
MATHEMATICA
w[x_] := ProductLog[x]; x = 1; y = 3; u = N[w[x] + w[y], 100]
RealDigits[u, 10][[1]] (* A299620 *)
RealDigits[LambertW[1] + LambertW[3], 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)
PROG
(PARI) lambertw(1) + lambertw(3) \\ G. C. Greubel, Mar 03 2018
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Mar 01 2018
STATUS
approved