What's the point of defining summation methods for divergent series? Do they have any connections to any other area of mathematics or physics? Is analytic continuation of complex analysis relevant to these things? How about p-adics?
I've started but haven't finished the physics lectures by Card Bender on mathematical physics, where he features perturbation theory prominently [2].
If someone could chime in on this, I would also be appreciative. Also if someone has better resources to learn about perturbation theory, I would also be appreciative.