Given that $s_t$ is a periodic function with period $d$, i.e. $s_{t-d} = s_t$, then time series seasonality can be characterised with harmonic sum:
$$ s_t = a_0 + \sum_{j=1}^k a_j \cos(\lambda_j t) + b_j\sin(\lambda_j t)$$
where $\lambda $ are fixed frequencies of the form $\frac{2\pi}{d}$ times some integer; $a_0, a_1, ..., a_k, b_1, ..., b_k$ are unknown parameters. Can someone explain why seasonality can be expressed as the afore-defined series?