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

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

Content Disclaimer

Informasi ini disarikan dari Wikipedia dan disajikan kembali untuk tujuan edukasi. Konten tersedia di bawah lisensi CC BY-SA 3.0. Kami tidak bertanggung jawab atas ketidakakuratan data yang bersumber dari kontribusi publik tersebut.

The information displayed on this website is sourced in part or in whole from Wikipedia and has been adapted for the purpose of restating it. We strive to provide accurate and relevant information, however:
There is no guarantee of absolute accuracy. Wikipedia is an open, collaborative project that can be edited by anyone, so information is subject to change.
It is not intended to constitute professional advice. The content displayed is for informational and educational purposes only. For important decisions (e.g., medical, legal, or financial), please consult a professional.
Content copyright. Wikipedia is licensed under the Creative Commons Attribution-ShareAlike License (CC BY-SA). This means that content may be reused with appropriate attribution and shared under a similar license.
Responsible use. Any risk arising from the use of information from this website is entirely the responsibility of the user.