Discrete analysis on a radial lattice

AbstractA discrete model for analytic functions is constructed using lattice points of the complex plane arranged in radial form. The discrete analytic functions are defined as solutions of a finite-difference approximation to the polar Cauchy-Riemann equations. The resulting discrete power z(n) (an analogue of zn) has a simple algebraic form (a direct analogue of ϱn exp{inθ}) and has some surprising properties. For example every discrete polynomial ∑0m anz(n) has a factorization in terms of the zeros of its classical counterpart ∑0m anzn every discrete entire function has a power series representation ∑ anz(n)