Function series

In calculus, a function series is a series, where the summands are not just real or complex numbers but functions.

Examples

Examples of function series include power series, Laurent series, Fourier series, etc.

Convergence

As for sequences of functions, and unlike for series of numbers, there exist many types of convergence for a function series, such as uniform convergence, pointwise convergence, almost everywhere convergence, etc.

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

See also

• Function space

References

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