Common, A.K and Sommen, F. (1994) Special Bi-Axial Monogenic Functions. Journal of Mathematical Analysis and Applications, 185 (1). pp. 189-206. ISSN 0022-247X.
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| Official URL http://dx.doi.org/10.1006/jmaa.1994.1241 |
Abstract
In this paper we extend our recent work on axial monogenic functions in R(m+1) to functions which are monogenic in bi-axially symmetric domains of R(p+q). We show that an integral transform of a wide class of holomorphic functions of a single complex variable gives monogenic functions of this type. It is demonstrated that these integral transforms are related to plane wave monogenic functions. A bi-axial monogenic exponential function is defined using the exponential function of a complex variable and bounds are obtained on its modulus. Bi-axially symmetric monogenic generating functions are used to define generalisations of Gegenbauer polynomials and Hermite polynomials. Finally, bi-axial power functions are constructed using the above integral transform. (C) 1994 Academic Press, Inc.
| Item Type: | Article |
|---|---|
| Subjects: | Q Science > QA Mathematics (inc Computing science) |
| Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science |
| Depositing User: | P. Ogbuji |
| Date Deposited: | 02 Jul 2009 15:46 |
| Last Modified: | 02 Jul 2009 15:46 |
| Resource URI: | http://kar.kent.ac.uk/id/eprint/20465 (The current URI for this page, for reference purposes) |
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