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Friday, October 30, 2015

**Abstract:** The class of discrete analytic functions is the discrete counterpart of the classical complex analytic functions. A noticeable peculiarity of discrete complex analysis is that the point-wise product of discrete analytic functions is not discrete analytic in general; for example, on the integer lattice in the complex plane, the functions z and z^2 are discrete analytic, but the function z^3 is not. Thus it is not an easy task to describe even the simplest algebraic discrete analytic functions, such as polynomials, rational functions or, even less, power series. Here we develop a basis of discrete analytic polynomials that allows power series expansion of discrete analytic functions.