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A299617
Decimal expansion of e^(W(1) + W(e)) = e/(W(1)*W(e)), where W is the Lambert W function (or PowerLog); see Comments.
3
4, 7, 9, 2, 9, 3, 6, 5, 9, 0, 1, 4, 2, 8, 1, 4, 0, 2, 5, 7, 2, 5, 8, 4, 7, 3, 7, 2, 3, 8, 2, 1, 0, 8, 6, 0, 1, 5, 9, 6, 7, 8, 6, 3, 9, 6, 2, 8, 4, 3, 7, 6, 3, 9, 1, 3, 6, 6, 9, 9, 8, 4, 6, 8, 1, 6, 8, 5, 7, 7, 9, 5, 1, 4, 5, 2, 0, 4, 4, 0, 1, 7, 7, 4, 8, 4
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^(W(1) + W(e)) = e/(W(1)*W(e)). See A299613 for a guide to related constants.
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function
EXAMPLE
e^(W(1) + W(e)) = 4.7929365901428140257258473723821086015...
MATHEMATICA
w[x_] := ProductLog[x]; x = 1; y = E;
N[E^(w[x] + w[y]), 130] (* A299617 *)
RealDigits[E/(LambertW[1]*LambertW[E]), 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)
PROG
(PARI) exp(1)/(lambertw(1)*lambertw(exp(1))) \\ G. C. Greubel, Mar 03 2018
CROSSREFS
Sequence in context: A010299 A201413 A021680 * A201931 A201504 A159898
KEYWORD
nonn,cons,easy
AUTHOR
Clark Kimberling, Mar 01 2018
STATUS
approved