A299632 Decimal expansion of 2*W(e/2), where W is the Lambert W function (or PowerLog); see Comments.

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

Offset: 0

Author

Clark Kimberling, Mar 13 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 2*W(e/2) = W(e^2/(2*W(e/2))) = 2 - log(4) - 2*log(W(e/2)). See A299613 for a guide to related sequences.

Examples

			2*W(e/2) = 1.3701538843091878920564989610752603...
		

Links

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

Crossrefs

Cf. A299613, A299632.

Programs

Mathematica

w[x_] := ProductLog[x]; x = E/2; y = E/2; u = N[w[x] + w[y], 100]
RealDigits[u, 10][[1]]  (* A299632 *)

PARI

2*lambertw(exp(1)/2) \\ Altug Alkan, Mar 13 2018