Function series

In calculus, a function series is a series where each of its terms is a function, not just a real or complex number.

Examples of function series include ordinary power series, Laurent series, Fourier series, Liouville-Neumann series, formal power series, and Puiseux series.

There exist many types of convergence for a function series, such as uniform convergence, pointwise convergence, and convergence almost everywhere. Each type of convergence corresponds to a different metric for the space of functions that are added together in the series, and thus a different type of limit.

The Weierstrass M-test is a useful result in studying convergence of function series.

• Function space

• Chun Wa Wong (2013) Introduction to Mathematical Physics: Methods & Concepts Oxford University Press p. 655