On Bivariate Jacobi Konhauser Polynomials

TL;DR

This paper introduces a new class of bivariate Jacobi Konhauser polynomials, explores their fundamental properties, and extends the analysis to associated Mittag-Leffler functions, advancing the theory of biorthogonal polynomials.

Contribution

The paper presents the first study of bivariate Jacobi Konhauser polynomials, including their properties and related special functions, expanding the framework of biorthogonal polynomial families.

Findings

Established biorthogonality, operational formulas, and generating functions for the polynomials.

Derived integral representations and transformations under Laplace, fractional integrals, and derivatives.

Introduced and analyzed the bivariate Jacobi Konhauser Mittag-Leffler functions.

Abstract

Recently, \"Ozarslan and Elidemir (2023) introduced a methodology for constructing two-variable biorthogonal polynomial families with the help of one-variable biorthogonal and orthogonal polynomial families. The primary objective of the paper is to introduce novel class of two-variable biorthogonal polynomials namley bivariate Jacobi Konhauser polynomials. We investigate several fundamental properties of these polynomials including their biorthogonality property, operational formula, generating function, and integral representation. Furthermore, We inverstigate their images under the Laplace transform, fractional integral and derivative operators. Corresponding to these polynomials, we define the new type bivariate Jacobi Konhauser Mittag Leffler (JKML) function and obtain the similar properties for them.