A240341 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) [imaginary part].

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

Offset

1,1

Links

Table of n, a(n) for n=1..100.

MathOverflow, On equation f(z+1)-f(z)=f'(z)

Formula

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

Imaginary part of -LambertW(-2, -1/e) - 1.

Example

7.461489285654...

Mathematica

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

Crossrefs

Cf. A199460, A240340.

Sequence in context: A345292 A198357 A371850 * A011204 A154018 A021138

Adjacent sequences: A240338 A240339 A240340 * A240342 A240343 A240344

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 04 2014

Status

approved