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A299626 Decimal expansion of 2*W(3), where W is the Lambert W function (or PowerLog); see Comments. 3
2, 0, 9, 9, 8, 1, 7, 7, 8, 9, 9, 2, 8, 0, 7, 9, 9, 1, 9, 9, 7, 7, 3, 9, 4, 1, 4, 1, 1, 0, 5, 7, 9, 5, 8, 0, 9, 1, 7, 8, 9, 3, 3, 8, 8, 7, 4, 1, 2, 6, 8, 2, 9, 0, 5, 8, 6, 5, 7, 4, 3, 1, 6, 6, 6, 3, 3, 2, 9, 8, 1, 0, 0, 8, 8, 8, 8, 8, 5, 9, 1, 5, 7, 7, 1, 3 (list; constant; graph; refs; listen; history; text; internal format)
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(3) =W(18/W(3)) = 2*(log 3 - log(W(3)). See A299613 for a guide to related sequences.
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function
EXAMPLE
3*W(3) = 2.0998177899280799199773941411...
MATHEMATICA
w[x_] := ProductLog[x]; x = 3; y = 3; u = N[w[x] + w[y], 100]
RealDigits[u, 10][[1]] (* A299626 *)
RealDigits[2*LambertW[3], 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)
PROG
(PARI) 2*lambertw(3) \\ G. C. Greubel, Mar 03 2018
CROSSREFS
Sequence in context: A083864 A154937 A037996 * A002741 A213322 A368703
KEYWORD
nonn,cons,easy
AUTHOR
Clark Kimberling, Mar 03 2018
STATUS
approved

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Last modified April 15 13:47 EDT 2024. Contains 371689 sequences. (Running on oeis4.)