The following function is defined over the interval $[-L, L]:$
$$ f(x)=p x^{4}+q x^{5} .$$
If it is expressed as a Fourier series,
$$f(x)=a_{0}+\sum_{n=1}^{\infty}\left\{a_{n} \sin \left(\frac{\pi x}{L}\right)+b_{n} \cos \left(\frac{\pi x}{L}\right)\right\},$$
which options amongst the following are true?
- $a_{n}, n=1,2, \cdots, \infty$ depend on $p$
- $a_{n}, n=1,2, \cdots, \infty$ depend on $q$
- $b_{n}, n=1,2, \cdots, \infty$ depend on $p$
- $b_{n}, n=1,2, \cdots, \infty$ depend on $q$