# Fourier sine and cosine series

In mathematics, particularly the field of calculus and Fourier analysis, the **Fourier sine and cosine series** are two mathematical series named after Joseph Fourier.

## Contents

## NotationEdit

In this article, *f* denotes a real valued function on which is periodic with period 2*L*.
The value of term c is L which is always taken as half of the total interval function *f* is defined in or we are concerned in .. In here we are using L instead of c .

## Sine seriesEdit

If f(x) is an odd function, then the Fourier Half Range sine series of f is defined to be

which is just a form of complete Fourier series with the only difference that and is zero, and the series is defined for half of the interval.

In the formula we have ....

- .

## Cosine seriesEdit

## RemarksEdit

This notion can be generalized to functions which are not even or odd, but then the above formulas will look different.

## See alsoEdit

## BibliographyEdit

- Byerly, William Elwood (1893). "Chapter 2: Development in Trigonometric Series".
*An Elementary Treatise on Fourier's Series: And Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics*(2 ed.). Ginn. p. 30. - Carslaw, Horatio Scott (1921). "Chapter 7: Fourier's Series".
*Introduction to the Theory of Fourier's Series and Integrals, Volume 1*(2 ed.). Macmillan and Company. p. 196.