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We study a generalized Chebyshev oscillator [1] associated with a pointinteraction for the discrete Schr\"odinger equation. Our goal is to find arealization of the annihilation operator for this oscillator by a differentialoperator. This realization can be used to obtain a differential equation forthe corresponding generalized Chebyshev polynomials [2]. This report is acontinuation of our work [1], [3].

Realization by a differential operator of the annihilation operator for generalized Chebyshev oscillator