Abstract
A 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 z n ) has a simple algebraic form (a direct analogue of ϱ n exp{ inθ}) and has some surprising properties. For example every discrete polynomial ∑ 0 m a n z ( n) has a factorization in terms of the zeros of its classical counterpart ∑ 0 m a n z n every discrete entire function has a power series representation ∑ a n z ( n) .
Full Text
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call