Lagrange Interpolating Formula for Discrete Analytic Function

The goal of present paper is the proof of existence Taylor expansion for discrete analytic functions, defined on a finite subset of the Gaussian plane. In particular, it is shown that any discrete analytic function define on the square coinsides with its discrete Lagrange interpolating polynomial. It is proved that the space of discrete analytic function on the square is isomorphic to the quotient of the space analytic functions on the disc by a principal ideal.