## Product of Sheffer sequences: properties and examples.(English)Zbl 1431.33014

Summary: This article is written with an objective to explore the product of two Sheffer sequences. This article is an attempt to explore such type of product which extends the possibility to consider hybrid type Sheffer polynomials. It is important to remark that although this product can be viewed as the umbral composition of two Sheffer sequences but the results related to this product cannot be deduced from the results of the Sheffer sequences. The set of this product of Sheffer sequences is also a non-abelian group and thus convoluting different members of Sheffer class allows us to consider a number of hybrid type special polynomials as its members. Certain results for this class including the quasi-monomiality and determinant form are established. The article concludes with the possibility of considering the product of $$n$$-Sheffer sequences.

### MSC:

 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 11B83 Special sequences and polynomials 05A15 Exact enumeration problems, generating functions 12E10 Special polynomials in general fields 11C20 Matrices, determinants in number theory
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