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

Published online by Cambridge University Press:  24 March 2003

D. CONSTALES  and
R. S. KRAUßHAR
D. CONSTALES
Affiliation:
Department of Mathematical Analysis, Ghent University, Building S-22, Galglaan 2, B-9000 Ghent, Belgiumdcons@world.std.com
R. S. KRAUßHAR
Affiliation:
Department of Mathematical Analysis, Ghent University, Building S-22, Galglaan 2, B-9000 Ghent, Belgiumkrauss@cage.rug.ac.be
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Abstract

Singly-periodic monogenic cotangent and cosecant functions are important to Clifford analysis because they are the building blocks of the Bergman and Szegö 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.

Keywords

30G35
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 67 , Issue 2 , April 2003 , pp. 401 - 416
Copyright
The London Mathematical Society 2003

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