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Decimal expansion of the constant 'lambda' such that exp(lambda*z) is the first nontrivial first quadrant complex solution of this form to the functional equation f(z+1)-f(z)=f'(z) [real part].
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%I #7 Dec 10 2016 19:34:13

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

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

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

%N Decimal expansion of the constant 'lambda' such that exp(lambda*z) is the first nontrivial first quadrant complex solution of this form to the functional equation f(z+1)-f(z)=f'(z) [real part].

%H MathOverflow, <a href="http://mathoverflow.net/questions/114875">On equation f(z+1)-f(z)=f'(z)</a>

%F First non-null solution to exp(lambda)-1=lambda in the first quadrant (real part).

%F Real part of -LambertW(-2, -1/e) - 1.

%e 2.088843015613...

%t lambda = -ProductLog[-2, -1/E] - 1; First[RealDigits[Re[lambda], 10, 100]]

%Y Cf. A199460, A240341.

%K nonn,cons

%O 1,1

%A _Jean-François Alcover_, Apr 04 2014