Abstract
The aim of this note is to find the explicit solution of four-point linear partial difference equations with variable coefficients. Three-point and four-point cases in quadrant and cone domains are considered and the boundary conditions, allowing the existence and the uniqueness of the solution, are detailed. The adopted procedure is a double iteration and the solution consists of a product of series, whose number of factors may be reduced successively by means of the indefinite sum operator of the difference calculus.
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