Fourier coefficients on closed and open intervals

Question

Let a function $f(x)$ be continuous, periodic, differentiable, and square-integrable on an open interval $(a,\,b)$. Will, its Fourier series coefficients change if it had all these qualities for a closed interval $[a,\,b]$. What about half-open and half-closed intervals $(a,\,b]$? What would be the difference in the series of the functions for all these intervals?