A299619 - OEIS

%I #8 Mar 04 2018 04:08:28

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

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

%U 0,2,7,8,6,1,6,3,1,0,9,1,0,5,1,1,6,6

%N Decimal expansion of e^(W(1) + W(1/e)) = (1/e)/(W(1)*W(1/e)), 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^(W(1) + W(1/e)) = (1/e)/(W(1)*W(1/e)).  See A299613 for a guide to related constants.

%H G. C. Greubel, <a href="/A299619/b299619.txt">Table of n, a(n) for n = 1..10000</a>

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

%e e^(W(1) + W(1/e)) = 2.3293932668427932248576309...

%t w[x_] := ProductLog[x]; x = 1; y = 1/E;

%t N[E^(w[x] + w[y]), 130]   (* A299619 *)

%t RealDigits[1/(E*LambertW[1]*LambertW[1/E]), 10, 100][[1]] (* _G. C. Greubel_, Mar 03 2018 *)

%o (PARI) exp(-1)/(lambertw(1)*lambertw(exp(-1))) \\ _G. C. Greubel_, Mar 03 2018

%Y Cf. A299613, A299618.

%K nonn,cons,easy

%O 1,1

%A _Clark Kimberling_, Mar 01 2018