I have a generalized quadratic Gauss sums, which is defiend as
$$S(a,b) = \sum_{n = 0}^Ne^{-j(an + bn^2)}$$
where $a\in(-\pi,\pi)$, $b\in(0,\pi)$ and $n$ is an integer. Now I am trying to approximate this summation by integeral via
$$S(a,b) \approx \int_{n=0}^N {e^{-j(an + bn^2)}dn}$$ when $N$ is a large number. My concern is, under what condition, such an approxiamtion holds?