Given a series of polynomials ${p_n}\left( x \right), n = 0,1,2, \ldots ,$ that are orthogonal in a range $[a,b]$, you can approximate a continuous function on that range as $$f(x) \sim\sum_{i=0}^{\infty} c_i p_n(x)$$
However, how would you find the series of coefficients $c_i$ for the series? For example, use the Laguerre or Hermite polynomials
From @QiaochuYuan's comment:
If the polynomials $p_n(x)$ are orthogonal with respect to a weight $w(x)$ on $[a,b]$, which means that if we define $\langle f, g \rangle = \int_a^b f(x) \overline{g(x)} w(x) \, dx$ then $\langle p_i, p_j \rangle = 0$ if $i \neq j$ and is positive otherwise, then the coefficient of $c_n$ in the expansion of a function $f$ is $\frac{ \langle f, p_n \rangle}{\langle p_n, p_n \rangle}$.
EDIT: For future reference, I found this article that explained it perfectly-- don't know how I forgot it.