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Decimal expansion of e^(W(1) + W(2)) = 2/(W(1)*W(2)), where W is the Lambert W function (or PowerLog); see Comments.
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%I #8 Mar 04 2018 04:11:25

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

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

%U 4,4,9,9,9,0,6,9,6,4,1,8,0,5,4,2,7,4

%N Decimal expansion of e^(W(1) + W(2)) = 2/(W(1)*W(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^(W(1) + W(2)) = 2/(W(1)*W(2)). See A299613 for a guide to related constants.

%H G. C. Greubel, <a href="/A299616/b299616.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(2)) = 4.13608129477801994342...

%t w[x_] := ProductLog[x]; x = 1; y = 2; N[E^(w[x] + w[y]), 130] (* A299616 *)

%t RealDigits[2/(LambertW[1]*LambertW[2]), 10, 100][[1]] (* _G. C. Greubel_, Mar 03 2018 *)

%o (PARI) 2/(lambertw(1)*lambertw(2)) \\ _G. C. Greubel_, Mar 03 2018

%Y Cf. A299613, A299615.

%K nonn,cons,easy

%O 1,1

%A _Clark Kimberling_, Mar 01 2018