Finite bivariate biorthogonal $N$-Konhauser polynomials

TL;DR

This paper introduces a new finite 2D biorthogonal polynomial set based on orthogonal and Konhauser polynomials, establishing connections with Laguerre-Konhauser polynomials and exploring their applications.

Contribution

It defines a novel finite bivariate biorthogonal polynomial set and links it to existing polynomial families, expanding the theoretical framework and potential applications.

Findings

Established connection with generalized Laguerre-Konhauser polynomials

Derived properties and relations of the new polynomial set

Presented potential applications in mathematical analysis

Abstract

A new set of finite 2D biorthogonal polynomials is defined using the finite orthogonal polynomials $N_{n}^{(p)}(w)$ and the Konhauser polynomials. We present a connection between this finite 2D biorthogonal set and the generalized Laguerre-Konhauser polynomials. Also, we obtain several applications of finite bivariate biorthogonal $N$-Konhauser polynomials.