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. 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 R {displaystyle mathbb {R} } which is periodic with period 2L.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 . 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 a 0 {displaystyle a_{0}} and a n {displaystyle a_{n}} is zero, and the series is defined for half of the interval.