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A299618
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Decimal expansion of W(1) + W(1/e), where w is the Lambert W function (or PowerLog); see Comments.
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4
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8, 4, 5, 6, 0, 7, 8, 3, 3, 1, 7, 0, 8, 5, 7, 6, 6, 8, 1, 0, 9, 3, 2, 7, 4, 0, 1, 2, 3, 3, 3, 3, 5, 7, 0, 5, 1, 9, 3, 2, 9, 3, 2, 7, 5, 8, 0, 6, 2, 5, 8, 2, 7, 3, 5, 8, 8, 3, 0, 9, 1, 8, 4, 7, 5, 8, 0, 7, 5, 1, 6, 8, 5, 4, 6, 6, 3, 4, 4, 6, 4, 8, 8, 5, 2, 6
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OFFSET
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0,1
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COMMENTS
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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/e) = W((1/e)(1/W(1)) + 1/W(1/e))) = - 1 - log(W(1)) - log(W(1/e)). See A299613 for a guide to related sequences.
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LINKS
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EXAMPLE
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W(1) + W(1/e) = 0.845607833170857668109327401233335...
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MATHEMATICA
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w[x_] := ProductLog[x]; x = 1; y = 1/E; u = N[w[x] + w[y], 100]
RealDigits[u, 10][[1]] (* A299618 *)
RealDigits[LambertW[1] + LambertW[1/E], 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)
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PROG
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(PARI) lambertw(1) + lambertw(exp(-1)) \\ G. C. Greubel, Mar 03 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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