CLOSED FORMULAS FOR SINGLY-PERIODIC MONOGENIC COTANGENT, COSECANT AND COSECANT-SQUARED FUNCTIONS IN CLIFFORD ANALYSIS

Singly-periodic monogenic cotangent and cosecant functions are important to Clifford analysis because they are the building blocks of the Bergman and Szeg? reproducing kernels for strip domains, that is, rectangular domains with a single bounded dimension. The paper establishes a wide range of explicit formulas for these functions, in terms of derivatives, of one-dimensional integrals, and of Fourier and plane wave multidimensional integrals. These results indicate how the elementary trigonometric functions $\cot(z)$, $\csc(z)$ and $\csc^2(z)$ are ramified into different entities when the setting is switched from complex analytic to Clifford monogenic.