Book on the Lambert W function.

Question

The Lambert W function is the inverse of function $x\mapsto xe^x$. It is traditionally denoted by $W(x)$. The function $W(x)$ is bivalued in interval $(-\frac{1}{e},0)$. See Wikpedia and Wolfram for more details.

QUESTION. Is there a book with a one chapter or several chapters devoted entirely to Lambert's W function?

By chapters it is "entirely devoted to Lambert's W function" I mean chapters containing at least one of the six iteins below:

1. Expansion, in Taylor series, of the W Lambert function around specific points $x_0\in (-\frac{1}{e},\infty)$ with the corresponding radius $r>0$ of convergence.

2. Expansion, continued fractions, of the W Lambert function in specific points $x_0\in (-\frac{1}{e},\infty)$.

3. A table of values $ W (x) $ of Lambert's W function when $ x $ assumes values $ x = 0,1,2,3, \ldots $

4. An iterative procedure or a well-defined algorithm to calculate the values $ W (x) $ to $ x $ belonging to an appropriate subset of $ (-\frac{1}{e},\infty)$.

5. Applications in solution of non linear equations $f(x)=g(x)$ with $x\in\mathbb{R}$,

6. Applications in solutions of ordinary differential equations,

Answer 1

I am not aware of any book containing such a chapter, but you might find interesting the article On the Lambert $W$ Function, by several authors (among whom Donald E. Knuth).