Although the generalized complex planes have the same form as the complex plane, theorems and concepts that have been proven true for complex numbers cannot necessarily be extended to dual and double numbers. In this paper, we explore analytic functions of a dual and double variable and disprove two Liouville theorems in these cases. We also modify a domain coloring scheme in order to visualize analytic functions of a generalized complex variable.
Michael Bolt, Department of Mathematics and Statistics, Calvin College
DenHartigh, Kyle and Flim, Rachel
"Liouville theorems in the Dual and Double Planes,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 12
, Article 4.
Available at: http://scholar.rose-hulman.edu/rhumj/vol12/iss2/4