Ji Eun Kim, Su Jin Lim, and Kwang Ho Shon in Department of Mathematics, Pusan National University, Busan 609-735, Republic of Korea, Abstract and Applied Analysis, Volume 2014 (2014), Article ID 654798, 8 pages,
http://dx.doi.org/10.1155/2014/654798, Received 11 December 2013; Revised 12 February 2014; Accepted 18 February 2014; Published 20 March 2014
Abstract: We define a new hypercomplex structure
of R^3 and a regular function with values in that structure. From the properties of regular functions, we research the exponential function on the reduced quaternion field and represent the corresponding Cauchy-Riemann equations in hypercomplex structures of R^3.