Problem #PRU-61456

Problems Calculus Functions of several variables

Problem

Let $f (x, y)$ be a harmonic function. Prove that the functions $Δ_{x} f (x, y) = f (x + 1, y) - f (x, y)$ and $Δ_{y} f (x, y) = f (x, y + 1) - f (x, y)$ will also be harmonic.

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