The density of a wrapped normal distribution is given by $$\frac{1}{\sigma \sqrt{2\pi} }\sum _{k=-\infty }^{\infty }\text{Exp}\left[\frac{-(\theta -\mu -2\pi k)^2}{2\sigma^2}\right]$$ Considering two density functions $f(x),\ g(x)$ of a wrapped normal distribution with respective parameters $\mu_1,\ \mu_2$ and $\sigma_1,\ \sigma_2$, is the product $h(x)=f(x)g(x)$ a density function of a wrapped normal distribution?