A299617 - OEIS

%I #8 Mar 04 2018 04:10:58

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

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

%U 7,7,9,5,1,4,5,2,0,4,4,0,1,7,7,4,8,4

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

%H G. C. Greubel, <a href="/A299617/b299617.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(e)) = 4.7929365901428140257258473723821086015...

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

%t N[E^(w[x] + w[y]), 130]   (* A299617 *)

%t RealDigits[E/(LambertW[1]*LambertW[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, A030178.

%K nonn,cons,easy

%O 1,1

%A _Clark Kimberling_, Mar 01 2018