I've a Fourier series up to the 3rd harmonic. It looks like this: f(x) = 7.833333335 - 0.327444444*cos(0.349*x) - 0.882182222*cos(0.698*x) + 0.0000355555*cos(1.047*x) - 5.150566667*sin(0.349*x) - 2.298188889*sin(0.698*x) - 1.154688889*sin(1.047*x)
$f(x)$ is presently defined only on $[0, 17]$ (since it was derived from practical harmonic analysis).
I'd like to expand the domain of $f(x)$.
Can I do this using analytic continuation? (Considering my function has no imaginary part) If yes, how? If no, how else may I expand its domain?