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In this paper, using operational rules, we derive some explicit expansion formulas associated with Brenke type polynomials. In particular, the corresponding connection and linearization coefficients are expressed either in terms of double sums or integral representations or sometimes in closed hypergeometric terms. The derived results are applied to Generalized Gould–Hopper and q-Laguerre polynomials. Some well-known duplication and convolution formulas are deduced as particular cases. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to introduce and investigate a new d-orthogonal family generalizing the Laguerre polynomial set. We use operational rules associated with corresponding lowering, raising and transfer operators to derive many related properties, namely, recurrence relation, d-orthogonality, functional vector of d-orthogonality, inversion and connection relations, differential equation, among others. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the discrete Hahn-classical d-orthogonal polynomial sets (and their iterated) by a difference distributional matrix equation satisfied by the associated d-dimensional functional vector, where the coefficient matrices are explicitly given. As a result we describe this set of polynomials via a structure relation. We illustrate the preceding results with some examples. [ABSTRACT FROM AUTHOR]

In this work, we prove that the zeros of the hyper-Bessel function are located onrays emanating from the origin with the positive real axis as ray, and that the onlyd-orthogonal Jensen polynomials associated with an entire function in the Laguerre–Pólya class are thed-orthogonal Laguerre polynomials. [ABSTRACT FROM AUTHOR]