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## Real Fourier-Series |

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z | overview |

The real Fourier series of a real -periodic function is an orthogonal expansion in terms of sines and cosines:

The type and rate of convergence of the series depends on the smoothness of . For example, sufficient for absolute convergence is that the series and converge.

A convergent Fourier series needs not to represent the true function value at every point. Usually, at a point of discontinuity, the series converges to the arithmetic mean of the left and right limits of . This explains the notation instead of , which emphasizes these convergence issues.

**see also:**

- Keyword: Fourier series

[Examples]

automatically generated 9/22/2016 |