In mathematics, particularly the field of calculus and Fourier analysis, the Fourier sine and cosine series are two mathematical series named after Joseph Fourier.
In this article, f denotes a real valued function on .
The Fourier sine series of f is defined to be
If f is continuous and , then the Fourier sine series of f is equal to f on , odd, and periodic with period .
The Fourier cosine series is defined to be
If f is continuous, then the Fourier cosine series of f is equal to f on , even, and periodic with period .
This notion can be generalized to functions which are not continuous.
Haberman, Richard. Applied Partial Differential Equations with Fourier Series and Boundary Value Problems (4th ed.). Pearson. pp. 97–113. ISBN 978-0130652430.