J.A. Marão, M.F. Borges
Department of Mathematics
UFMA - Federal University of Maranhão
65085-580, Maranhão, BRAZIL
UNESP - São Paulo State University
S.J. Rio Preto Campus
15054-000, São José do Rio Preto, BRAZIL

Abstract. In recent years quaternionic functions have been an intense and prosperous object of research, and important results were determined [#!1!#]-[#!6!#]. Some of these results are similar to well known cases in one complex variable, op. cit. [#!5!#], [#!6!#]. In this paper the hypercomplex expansion of a function in a power series as well as determination of a Liouville's type theorem have been investigated to the quaternionic functions. In this case, it is observed that the Liouville's type theorem is true for second order derivatives, which differs from its classical version.

Received: April 23, 2011

AMS Subject Classification: 30G99, 30E99

Key Words and Phrases: quaternions series, hypercomplex, quaternions

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