Hermite-based Appell polynomials: Properties and applications. (English) Zbl 1158.33004
The authors use operational methods to introduce Hermite-based Appell polynomials and discuss their properties and applications. The operational methods were developed by G. Dattoli and his co-workers to investigate some families of orthogonal polynomials in two or more variables or/and multi-index cases. The authors also introduce Hermite-Laguere and Hermite-Sister Celine’s polynomials as members of the family of Hermite-based Sheffer polynomials. We mention that the Sheffer polynomials include Appell polynomials as a special case along with the underlying operational formalism and offer a powerfull tool for investigation of the properties of a wide class of polynomials.
Reviewer: Chrysoula G. Kokologiannaki (Patras)
MSC:
| 33C50 | Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable |
| 33C65 | Appell, Horn and Lauricella functions |
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