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A299614
Decimal expansion of e^(2*A030178) = e^(2*W(1)) = (1/W(1))^2, where W is the Lambert W function (or PowerLog); see Comments.
2
3, 1, 0, 8, 9, 5, 4, 7, 6, 3, 5, 7, 9, 9, 3, 6, 1, 8, 5, 4, 8, 0, 9, 4, 5, 4, 0, 5, 4, 2, 4, 5, 6, 9, 3, 0, 7, 8, 5, 0, 1, 5, 8, 1, 2, 1, 5, 7, 4, 0, 8, 0, 7, 7, 1, 5, 5, 1, 0, 9, 7, 0, 4, 4, 2, 6, 5, 0, 1, 6, 1, 5, 4, 9, 3, 5, 9, 0, 1, 3, 3, 8, 7, 9, 6, 5
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(1)) = (W(1))^(-2). See A299613 for a guide to related constants.
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function
EXAMPLE
e^(2*W(1)) = 3.1089547635799361854809454054...
MATHEMATICA
w[x_] := ProductLog[x]; x = 1; y = 1;
N[E^(w[x] + w[y]), 130] (* A299614 *)
RealDigits[(1/LambertW[1])^2, 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)
PROG
(PARI) (1/lambertw(1))^2 \\ G. C. Greubel, Mar 03 2018
CROSSREFS
Cf. A299613.
Sequence in context: A360829 A078521 A194938 * A135871 A126178 A094753
KEYWORD
nonn,cons,easy
AUTHOR
Clark Kimberling, Mar 01 2018
STATUS
approved