IJPAM: Volume 44, No. 3 (2008)

ON GENERALIZED EULER POLYNOMIALS
IN CLIFFORD ANALYSIS

H.R. Malonek$^1$, G. Tomaz$^2$
$^1$Department of Mathematics
University of Aveiro
Aveiro, 3810-193, PORTUGAL
e-mail: hrmalon@ua.pt
$^2$Department of Mathematics
Polytechnical Institute of Guarda
Guarda, 6300-559, PORTUGAL
e-mail: gtomaz@ipg.pt


Abstract.The aim of this paper is to obtain a multi-dimensional generalization of the well known Euler polynomials in the context of Clifford Analysis. The generalized Euler polynomials are achieved via a generating function. They are special hypercomplex holomorphic functions with properties analogous to those of the classical polynomials. Furthermore, a hypercomplex polynomial Euler matrix is defined using a hypercomplex Pascal matrix.

Received: March 6, 2008

AMS Subject Classification: 05A19, 11B68, 30G35

Key Words and Phrases: hypercomplex Euler polynomials, Euler numbers, hypercomplex Euler matrix

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 44
Issue: 3