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.

$\int _{0}^{L}e^{2\pi {}inx/L}e^{-2\pi {}imx/L}{\textrm {d}}x={\begin{cases}L,\qquad {}n=m\\0,\qquad {}n\neq {}m\end{cases}}$

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