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A299627
Decimal expansion of e^(2*W(3)) = 9/(W(3))^2, where W is the Lambert W function (or PowerLog); see Comments.
3
8, 1, 6, 4, 6, 8, 2, 0, 8, 9, 7, 1, 2, 8, 4, 0, 5, 9, 1, 0, 9, 3, 8, 8, 7, 3, 7, 1, 1, 5, 6, 5, 4, 2, 2, 8, 7, 6, 6, 4, 4, 9, 4, 1, 9, 9, 6, 0, 4, 6, 7, 3, 7, 3, 4, 7, 7, 1, 0, 8, 1, 6, 3, 2, 1, 5, 6, 7, 1, 7, 8, 1, 2, 3, 1, 1, 7, 7, 9, 2, 3, 3, 8, 4, 3, 3
OFFSET
1,1
COMMENTS
The Lambert W function satisfies the functional equation e^(W(x) + W(y)) = x*y/(W(x)*W(y)) for x and y greater than -1/e, so that e^(2*W(3)) = 9/(W(3))^2. See A299613 for a guide to related constants.
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function
EXAMPLE
e^(2*W(3)) = 8.1646820897128405910938873711...
MATHEMATICA
w[x_] := ProductLog[x]; x = 3; y = 3;
N[E^(w[x] + w[y]), 130] (* A299627 *)
RealDigits[(3/LambertW[3])^2, 10, 100][[1]] (* G. C. Greubel, Mar 06 2018 *)
PROG
(PARI) (3/lambertw(3))^2 \\ G. C. Greubel, Mar 06 2018
CROSSREFS
Sequence in context: A033812 A019717 A007404 * A157697 A281785 A240982
KEYWORD
nonn,cons,easy
AUTHOR
Clark Kimberling, Mar 03 2018
STATUS
approved