Elementary and Miscellaneous Analysis

We have attempted to make the title of this chapter broad enough to encompass all the results contained therein. More precisely, we have placed in this chapter those results connected with analysis that are either very elementary or do not seem to fit in any other chapter. It must be admitted that some entries in this chapter are not particularly interesting. Some entries are trivial or are well known to almost all mathematicians, and one may ask why Ramanujan recorded them. There are at least two rejoinders. First, the third notebook appears to contain findings from Ramanujan’s youth, possibly as early as 1903, in addition to theorems perhaps recorded in England. Second, the recording of such items as the definition of a limit and the connection between a function’s singularities and the radius of convergence of its power series evince the absence of theoretical analysis in Ramanujan’s training.