$\displaystyle Dirichlet’s\ conditions\ for\ a\ function\ f(x)\ to\ have\ a\ Fourier\ series\ over\ (a,b): \\[2ex] $

$ \displaystyle i)\ f(x) , \ and\ its\ integrals\ are\ finite\ and\ single\ valued. \\[2ex] $

$\displaystyle ii)\ f(x) , \ has\ finite\ numbers\ of\ discontinuities. \\[2ex] $

$\displaystyle iii)f(x)\ has\ finite\ number\ of\ maxima\ and\ minima. \\[2ex] $

$\displaystyle In\ the\ interval\ (-\pi{},\pi{}),\\[2ex] f(x)=sinx\ is\ not\ single\ valued\ For\ example,\sin\frac{\pi{}}{3}=\sin\frac{2\pi{}}{3} \\[2ex] \displaystyle\\[2ex] So,\ f(x)\ cannot\ be\ expanded\ in\ Fourier\ series\ in\ (-\pi{},\pi{}).\ \ \ \\[2ex]$