Certain results on a hybrid class of the Boas–Buck polynomials

Abstract

Abstract This article aims to introduce a hybrid family of 2-variable Boas–Buck-general polynomials by taking Boas–Buck polynomials as a base with the 2-variable general polynomials. These polynomials are framed within the context of the monomiality principle, and their properties are established. Further, we investigate some members belonging to this family. A general method to express connection coefficients explicitly for the Boas–Buck general polynomial sets is presented. Carlitz theorem for mixed generating functions is also extended to these polynomials. The shapes are shown and zeros are computed for these polynomials using Mathematica software.

Keywords

• Boas–Buck polynomials
• 2-variable general polynomials
• Monomiality principle
• Operational techniques
• Carlitz theorem
• Connection coefficients