Function series

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


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


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[edit]


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