The sine-cosine form of the fourier series is given by:
$$ s_{\scriptscriptstyle N}(x) = \frac{a_0}{2} + \sum_{n=1}^N \left(a_n \cos\left(\tfrac{2\pi}{P} nx \right) + b_n \sin\left(\tfrac{2\pi}{P} nx \right) \right) $$
I was wondering if there is something similar for the hyperbolic trigonemetric functions
$$ s_{\scriptscriptstyle N}(x) = \frac{a_0}{2} + \sum_{n=1}^N \left(a_n \boxed{\cosh}\left(\tfrac{2\pi}{P} nx \right) + b_n \boxed{\sinh}\left(\tfrac{2\pi}{P} nx \right) \right)$$
Seems kind of useless because the hyperbolic functions are not really periodic in $\mathbb{R}$.