A299618 Decimal expansion of W(1) + W(1/e), where w is the Lambert W function (or PowerLog); see Comments.

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

Offset: 0

Author

Clark Kimberling, Mar 01 2018

Keywords

• nonn
• cons
• easy

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/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.

Examples

			W(1) + W(1/e) = 0.845607833170857668109327401233335...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A299613, A299619.

Programs

Mathematica

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 *)

PARI

lambertw(1) + lambertw(exp(-1)) \\ G. C. Greubel, Mar 03 2018