 ##  [Fourier Series](/index.php/fourier-series) 

  ##  [Fourier Series](https://natural.quantumdictionary.io/fourier-series-0) 

  
 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/index.php/topic-specific-dictionaries/natural-formal-sciences)


**Natural &amp; Formal Sciences Dictionary**

 
Definition

A representation of a periodic function on an interval as a (possibly infinite) sum of sinusoidal basis functions or complex exponentials with discrete frequencies and corresponding coefficients.

 
 ##  [Fourier Series](https://puremath.quantumdictionary.io/fourier-series-1) 

  
 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/index.php/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics &amp; Logic -

**Pure Mathematics Dictionary**

 
Definition

The representation of a periodic function as a (possibly infinite) sum of sines and cosines or complex exponentials whose coefficients are determined by inner products with the orthogonal exponential basis on the circle.