A299619 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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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(1/e)) = (1/e)/(W(1)*W(1/e)). See A299613 for a guide to related constants.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Lambert W-Function

Example

e^(W(1) + W(1/e)) = 2.3293932668427932248576309...

Mathematica

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 *)

Prog

(PARI) exp(-1)/(lambertw(1)*lambertw(exp(-1))) \\ G. C. Greubel, Mar 03 2018

Crossrefs

Cf. A299613, A299618.

Sequence in context: A349972 A163204 A364895 * A215269 A352485 A356092

Adjacent sequences: A299616 A299617 A299618 * A299620 A299621 A299622

Keyword

nonn,cons,easy

Author

Clark Kimberling, Mar 01 2018

Status

approved