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%I #8 Mar 04 2018 04:12:39
%S 5,5,0,2,5,4,6,6,0,4,2,2,0,7,2,4,0,7,5,3,1,1,2,6,8,1,3,5,9,4,9,3,2,6,
%T 0,1,9,5,5,3,8,4,3,4,8,0,0,7,2,8,3,1,7,5,2,0,4,0,1,5,0,2,8,4,7,3,0,5,
%U 8,9,6,0,9,9,9,6,7,2,8,7,6,7,4,0,2,7
%N Decimal expansion of e^(2*W(2)) = 4/(W(2))^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(2)) = 4/(W(2))^2. See A299613 for a guide to related constants.
%H G. C. Greubel, <a href="/A299625/b299625.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^(2*W(2)) = 5.50254660422072407531126813594932...
%t w[x_] := ProductLog[x]; x = 2; y = 2;
%t N[E^(w[x] + w[y]), 130] (* A299625 *)
%t RealDigits[(2/LambertW[2])^2, 10, 100][[1]] (* _G. C. Greubel_, Mar 03 2018 *)
%o (PARI) (2/lambertw(2))^2 \\ _G. C. Greubel_, Mar 03 2018
%Y Cf. A299613, A299624.
%K nonn,cons,easy
%O 1,1
%A _Clark Kimberling_, Mar 03 2018
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