Special Bi-Axial Monogenic Functions

Common, Alan K. and Sommen, F. (1994) Special Bi-Axial Monogenic Functions. Journal of Mathematical Analysis and Applications, 185 (1). pp. 189-206. ISSN 0022-247X. (The full text of this publication is not available from this repository)

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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: 14 May 2014 14:42
Resource URI: http://kar.kent.ac.uk/id/eprint/20465 (The current URI for this page, for reference purposes)
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