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The q-Hermite I-Sobolev type polynomials of higher order are consider fortheir study. Their hypergeometric representation is provided together withfurther useful properties such as several structure relations which give riseto a three-term recurrence relation of their elements. Two differentq-difference equations satisfied by the q-Hermite I-Sobolev type polynomials ofhigher order are also established.

On second order q-difference equations for high-order Sobolev-type q-Hermite orthogonal polynomials