OFFSET
0,2
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 2*W(3/2) =W(e^2/2)/(1/W(e/2)) = 2 - log(4) - 2 log(W(e/2)). See A299613 for a guide to related sequences.
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function
EXAMPLE
2*W(e/2) = 1.3701538843091878920564989610752603...
MATHEMATICA
w[x_] := ProductLog[x]; x = E/2; y = E/2; u = N[w[x] + w[y], 100]
RealDigits[u, 10][[1]] (* A299632 *)
PROG
(PARI) 2*lambertw(exp(1)/2) \\ Altug Alkan, Mar 13 2018
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Mar 13 2018
STATUS
approved