On a difference equation with holomorphic coefficients generated by a hexagon

{Let $D$ be a hexagon with two straight and four right angles. We consider a seven-element difference equation with holomorphic coefficients generated by this hexagon. A method for regularizing this equation is proposed. The solution is sought in the class of functions holomorphic outside the "half" of the boundary $\partial D$ and vanishing at infinity. It is represented as a Cauchy-type integral over the "half" of the boundary with an unknown density. Applications to the problem of moments for entire functions of exponential type (e.f.e.t.) are indicated.