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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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.
|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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