A299633 Decimal expansion of e^(2*W(e/2)) = (e^2/4)/(W(e/2))^2, where W is the Lambert W function (or PowerLog); see Comments.

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Offset: 1

Author

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

Examples

			e^(2*W(e/2)) = 3.9359563307913488100211988489777007...
		

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; N[E^(w[x] + w[y]), 130]   (* A299633 *)

PARI

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