||The year 2016 marks 20 years since the publication of the paper
"On the Lambert W function". As will be pointed out, the function was
studied before 1996, but this publication has proved to be the most cited
reference. The talk will review some of the decisions made in defining
the function, particularly in defining its branches.
The talk will present some of the interesting and beautiful properties
of the function, including recent work that improves on the results in
the original papers. Specifically, expressions for derivatives and
series expansions, the role of differences between branches,
the convergence of series expansions. Some comments on implications
for computer algebra systems will also be made.