Monogenic generalized trigonometric and elliptic functions in Clifford analysis
by
Rolf Soeren Krausshar
Dep. of Math. Analysis, University of Ghent (Belgium)

Based on hypercomplex Eisenstein series we construct monogenic generalizations of the complex analytic tangent, cotangent, secant and cosecant function and the elliptic functions in Clifford analysis. We discuss some basic properties and show that all these functions can be characterized as solutions of certain functional equations, provided the singular parts are given.
We further show that any arbitrary p-fold periodic meromorphic function in R^k+1, where p is an element of {1, ... , k+1}, can be represented up to an entire function by a finite sum of monogenic Eisenstein series.

Date received: February 23, 2001