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%I #8 Mar 04 2018 04:13:26
%S 2,5,0,6,4,7,4,0,4,2,6,6,3,8,9,8,8,9,9,4,7,4,4,8,5,8,1,5,3,1,8,9,4,1,
%T 7,1,7,4,9,6,4,0,2,3,4,2,3,3,5,7,4,1,5,8,8,0,8,9,8,9,5,4,2,8,6,6,0,1,
%U 8,7,2,3,8,8,2,0,4,3,8,5,6,9,1,6,9,0
%N Decimal expansion of e^(W(1) + W(1/2)) = (1/2)/(W(1)*W(1/2)), 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(1/2)) = (1/2)/(W(1)*W(1/2)). See A299613 for a guide to related constants.
%H G. C. Greubel, <a href="/A299623/b299623.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(1/2)) = 2.506474042663898899474485815318941717...
%t w[x_] := ProductLog[x]; x = 1; y = 1/2;
%t N[E^(w[x] + w[y]), 130] (* A299623 *)
%t RealDigits[1/(2*LambertW[1]*LambertW[1/2]), 10, 100][[1]] (* _G. C. Greubel_, Mar 03 2018 *)
%o (PARI) 1/(2*lambertw(1)*lambertw(1/2)) \\ _G. C. Greubel_, Mar 03 2018
%Y Cf. A299613, A299622.
%K nonn,cons,easy
%O 1,1
%A _Clark Kimberling_, Mar 03 2018
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