Mathematical Methods in the Applied Sciences vol:25 issue:16-18 pages:1507-1526
In this paper, we consider rectangular domains in real Euclidean spaces of dimension at least 2, where
the sides can be finite, semi-infinite, or fully infinite. The Bergman reproducing kernel for the space of monogenic and square integrable functions on such a domain is obtained in closed form as a finite sum of monogenic multiperiodic functions. The reproducing property leads to an estimate of the first derivative of the single-periodic cotangent function in terms of the classical real-valued Eisenstein series.