A299627 - OEIS

%I #15 Feb 16 2025 08:33:53

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

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

%U 1,7,8,1,2,3,1,1,7,7,9,2,3,3,8,4,3,3

%N Decimal expansion of e^(2*W(3)) = 9/(W(3))^2, where W is the Lambert W function (or PowerLog); see Comments.

%C 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(3)) = 9/(W(3))^2.  See A299613 for a guide to related constants.

%H G. C. Greubel, <a href="/A299627/b299627.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>

%e e^(2*W(3)) = 8.1646820897128405910938873711...

%t w[x_] := ProductLog[x]; x = 3; y = 3;

%t N[E^(w[x] + w[y]), 130]   (* A299627 *)

%t RealDigits[(3/LambertW[3])^2, 10, 100][[1]] (* _G. C. Greubel_, Mar 06 2018 *)

%o (PARI) (3/lambertw(3))^2 \\ _G. C. Greubel_, Mar 06 2018

%Y Cf. A299613, A299626.

%K nonn,cons,easy

%O 1,1

%A _Clark Kimberling_, Mar 03 2018