Abstract
The intended objective of this paper is to introduce a new class of the hybrid q-Sheffer polynomials by means of the generating function and series definition. The determinant definition and other striking properties of these polynomials are established. Certain results for the continuous q-Hermite-Appell polynomials are obtained. The graphical depictions are performed for certain members of the hybrid q-Sheffer family. The zeros of these members are also explored using numerical simulations. Finally, the orthogonality condition for the hybrid q-Sheffer polynomials is established.
Highlights
The intended objective of this paper is to introduce a new class of the hybrid q-Sheffer polynomials by means of the generating function and series definition
The orthogonal polynomials in general and the classical orthogonal polynomials in particular have been the objects of extensive works
The classical orthogonal polynomials constitute a very important and interesting set of special functions and of orthogonal polynomials. They are very interesting mathematical objects that have attracted the attention of mathematicians
Summary
Abstract: The intended objective of this paper is to introduce a new class of the hybrid q-Sheffer polynomials by means of the generating function and series definition. The determinant definition and other striking properties of these polynomials are established. Certain results for the continuous q-Hermite-Appell polynomials are obtained. The graphical depictions are performed for certain members of the hybrid q-Sheffer family. The zeros of these members are explored using numerical simulations. The orthogonality condition for the hybrid q-Sheffer polynomials is established
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