Analytic Power Series

In this video we look at analytic power series, those that converge on some open interval about 0. They represent functions and many things you can do with functions are naturally mimicked with power series. In this video, we see how such operations work. In particular, we see how there are natural ways to add, multiply and differentiate power series, and they correspond to adding multiplying and differentiating the functions they converge, at least on their interval of convergence. This gives a new way to study functions.