A346205 Decimal expansion of solution to LambertW(-x) - LambertW(-1,-x) = 2.

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

Offset

0,1

Links

Table of n, a(n) for n=0..109.

Formula

Equals exp(-coth(1))/sinh(1) = exp(-A073747)/A073742.

Equals (coth(1)-1)*exp(1-coth(1)) = (A073747-1)*exp(1-A073747).

Equals (coth(1)+1)/exp(1+coth(1)) = (A073747+1)/exp(1+A073747).

Equals 2/(e^2-1)*exp(2/(1-e^2)) = 2/(A072334^2-1)*exp(2/(1-A072334^2)).

Example

0.2288989481961786412366361253722...

Mathematica

x/.FindRoot[LambertW[-x]-LambertW[-1, -x]==2, {x, 0.1, 0.3}, WorkingPrecision -> 110]

Prog

(PARI) exp(-cotanh(1))/sinh(1)

Crossrefs

Cf. A072334, A073742, A073747.

Sequence in context: A187791 A245235 A151924 * A343984 A268342 A058524

Adjacent sequences: A346202 A346203 A346204 * A346206 A346207 A346208

Keyword

nonn,cons

Author

Gleb Koloskov, Jul 10 2021

Status

approved