|
|
A299622
|
|
Decimal expansion of W(1) + W(1/2), where W is the Lambert W function (or PowerLog); see Comments.
|
|
3
|
|
|
9, 1, 8, 8, 7, 7, 0, 0, 1, 6, 5, 8, 9, 7, 9, 6, 9, 9, 0, 2, 4, 8, 7, 7, 9, 6, 3, 1, 4, 0, 3, 0, 6, 6, 1, 4, 9, 2, 5, 2, 8, 0, 0, 0, 2, 7, 0, 3, 6, 2, 4, 3, 1, 2, 1, 8, 1, 7, 7, 4, 9, 2, 5, 3, 3, 3, 0, 0, 6, 4, 0, 3, 8, 0, 7, 0, 2, 3, 2, 7, 7, 5, 9, 0, 0, 5
(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 W(1) + W(1/2) = W((1/2)(W(1/W(1)) + 1/W(1/2)) = - log(2) - log(W(1)) - log(W(1/2)). See A299613 for a guide to related sequences.
|
|
LINKS
|
|
|
EXAMPLE
|
W(1) + W(1/2) = 0.918877001658979699024877963140306614925280002...
|
|
MATHEMATICA
|
w[x_] := ProductLog[x]; x = 1; y = 1/2; u = N[w[x] + w[y], 100]
RealDigits[u, 10][[1]] (* A299622 *)
RealDigits[LambertW[1] + LambertW[1/2], 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|