A299625 Decimal expansion of e^(2*W(2)) = 4/(W(2))^2, where W is the Lambert W function (or PowerLog); see Comments.

5, 5, 0, 2, 5, 4, 6, 6, 0, 4, 2, 2, 0, 7, 2, 4, 0, 7, 5, 3, 1, 1, 2, 6, 8, 1, 3, 5, 9, 4, 9, 3, 2, 6, 0, 1, 9, 5, 5, 3, 8, 4, 3, 4, 8, 0, 0, 7, 2, 8, 3, 1, 7, 5, 2, 0, 4, 0, 1, 5, 0, 2, 8, 4, 7, 3, 0, 5, 8, 9, 6, 0, 9, 9, 9, 6, 7, 2, 8, 7, 6, 7, 4, 0, 2, 7

Offset: 1

Author

Clark Kimberling, Mar 03 2018

Keywords

• nonn
• cons
• easy

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^(2*W(2)) = 4/(W(2))^2. See A299613 for a guide to related constants.

Examples

			e^(2*W(2)) = 5.50254660422072407531126813594932...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Lambert W-Function

Crossrefs

Cf. A299613, A299624.

Programs

Mathematica

w[x_] := ProductLog[x]; x = 2; y = 2;
N[E^(w[x] + w[y]), 130]   (* A299625 *)
RealDigits[(2/LambertW[2])^2, 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)

PARI

(2/lambertw(2))^2 \\ G. C. Greubel, Mar 03 2018