Generalized form of 2D-Laguerre polynomials

Abstract

The goal of this research is to present and investigate a novel class of 2D-Laguerre polynomials, which contains some well-known 2D-polynomials as special cases.We discuss its numerous features, including integral representations, operational identities, the monomiality principle, generating functions, and linkages to Appll functions of two variables and Lauricella functions of r-variables. Finally, we raise relevant issues for further research.

Keywords:

• Laguerre 2D polynomials
• Rodrigues and operational formulas
• lowering and raising operators
• generating functions
• Appell and Lauricella functions

2020 Mathematics Subject Classification:

• 33C45
• 33C65
• 33C90
• 26A33

Acknowledgments

We thank the anonymous reviewers for their valuable suggestions, which made the presentation of the paper more readable.

Data availability

The datasets generated during and/or analyzed during the current study are available from the references included in this article and from the corresponding author on reasonable request.

Disclosure statement

No potential conflict of interest was reported by the author(s).