There are a number of gems in this chapter from Ramanujan’s second notebook. One is an asymptotic expansion of
when m, n and
tend to infinity. A second is two terms of the asymptotic expansion of
(x) is a function analytic and nonvanishing for
’(x) are positive for
where M is a positive constant. Many other interesting results, too numerous to mention here, were stated by Ramanujan, and are either proved in this paper, or a reference is given to a proof or statement in the literature.