Science:Math Exam Resources/Courses/MATH307/December 2010/Question 06 (a)/Hint 1

Recall that the functions

${\displaystyle }{e}^{2\pi inx/L}$

are an orthogonal basis for square integrable functions, i.e.

$\underset{0}{\overset{L}{\int }}{e}^{2\pi inx/L}{e}^{-2\pi imx/L}\text{d}x=\{\begin{array}{l}L,n=m\\ 0,n\ne m\end{array}$

How can we use this orthogonality to get the coefficients in the series?