I consider the Lerch-Hurwitz or periodic zeta function as covariance function of a periodic continuous-time stationary stochastic process. The function can be parametrized with a continuous index $\nu$ which regulates the continuity and differentiability properties of the process in a way completely analogous to the parameter $\nu$ of the Mat\'ern class of covariance functions. This makes the periodic zeta a good companion to add a power-law prior spectrum seasonal component to a Mat\'ern prior for Gaussian process regression. It is also a close relative of the circular Mat\'ern covariance, and likewise can be used on spheres up to dimension three. Since this special function is not generally available in standard libraries, I explain in detail the numerical implementation.

翻译：我认为Lerch-Hurwitz 或定期 zeta 函数是定期连续固定式随机过程的共变函数。 该函数可以用一个连续的指数 $\ nu$ 来进行平衡, 以与 Mat\'ern 类共变函数的参数 $\ nu$ 完全相似的方式调节该过程的连续性和差异性。 这样, 定期 zeta 就可以作为良好的伴体, 在 Gaussian 进程回归之前的 Mat\' ern 中添加一个电源法前频谱季节性组件。 该函数也是该循环 Mat\ ern 共变函数的近亲关系, 并且同样可以用于第三维的球体上。 由于该特殊功能一般不在标准图书馆中可用, 我详细解释数字执行方式 。