Given a function $f(x)$, composed with continuous frequencies in certain interval $[-m,m]$,\begin{equation} f(x) = \frac{1}{a}\int_{-m}^{+m} \hat{f}\Big(\frac{\xi}{a}\Big)e^{\frac{i2\pi x\xi} {a}}d\xi; m\in \mathbb{N} \end{equation} and, if it is to be approximated with only integer frequencies, i.e Fourier series, what is the error $\varDelta_{|n|\leq|m|} = \tilde{f}(n/a)-\hat{f}(n/a)$ at integer frequencies, given \begin{equation} \tilde{f}(n/a)= \int_{-a/2}^{a/2} f(x) e^{\frac{-i2\pi n x}{a}} dx\end{equation}
is this anyhow connected to fractional Fourier transforms?