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 W(1) + W(1/2) = W((1/2)(W(1/W(1)) + 1/W(1/2)) = - log(2) - log(W(1)) - log(W(1/2)). 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
W(1) + W(1/2) = 0.918877001658979699024877963140306614925280002...
MATHEMATICA
w[x_] := ProductLog[x]; x = 1; y = 1/2; u = N[w[x] + w[y], 100]
RealDigits[u, 10][[1]] (* A299622 *)
RealDigits[LambertW[1] + LambertW[1/2], 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)
PROG
(PARI) lambertw(1) + lambertw(1/2) \\ G. C. Greubel, Mar 03 2018
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Mar 03 2018
STATUS
approved