We always talk about series being divergent or convergent. In elementary maths, we are very much interested in convergent series: we perform calculus, use them for approximations, use them as functions, and so on. As a result, there is so much to say about convergent series.
Just a question, without the need for substantive mathematical depth, do we have ever had analysis on divergent series? What can we do with them? Is there research being performed on them? What would be the themes, topics (even if they are just a quick overview/general background) on what they are about.
I am just interested to know.