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A299619
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Decimal expansion of e^(W(1) + W(1/e)) = (1/e)/(W(1)*W(1/e)), where W is the Lambert W function (or PowerLog); see Comments.
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3
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2, 3, 2, 9, 3, 9, 3, 2, 6, 6, 8, 4, 2, 7, 9, 3, 2, 2, 4, 8, 5, 7, 6, 3, 0, 9, 1, 5, 6, 2, 7, 5, 2, 1, 9, 4, 3, 5, 7, 7, 4, 3, 9, 1, 9, 8, 0, 2, 3, 3, 3, 1, 5, 1, 3, 4, 6, 7, 1, 4, 9, 2, 5, 2, 4, 7, 2, 6, 0, 2, 7, 8, 6, 1, 6, 3, 1, 0, 9, 1, 0, 5, 1, 1, 6, 6
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OFFSET
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1,1
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COMMENTS
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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(1/e)) = (1/e)/(W(1)*W(1/e)). See A299613 for a guide to related constants.
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LINKS
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EXAMPLE
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e^(W(1) + W(1/e)) = 2.3293932668427932248576309...
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MATHEMATICA
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w[x_] := ProductLog[x]; x = 1; y = 1/E;
N[E^(w[x] + w[y]), 130] (* A299619 *)
RealDigits[1/(E*LambertW[1]*LambertW[1/E]), 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)
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PROG
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(PARI) exp(-1)/(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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