Function series

Short description: Mathematical series

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

## Contents

* 1 Examples
* 2 Convergence
* 3 See also
* 4 References

## Examples

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

## Convergence

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.

## See also

* Function space

## References

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

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