Title: On Bivariate Jacobi Konhauser Polynomials Show Chinese title

Title: 关于二元雅可比Konhauser多项式

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. Show Chinese abstract

Abstract: 最近，Özarslan和Elidemir（2023）引入了一种方法，借助一变量双正交和正交多项式族来构造两变量双正交多项式族。 本文的主要目标是介绍一类新的两变量双正交多项式，即双变量雅可比Konhauser多项式。 我们研究了这些多项式的几个基本性质，包括它们的双正交性、运算公式、生成函数和积分表示。 此外，我们研究了它们在拉普拉斯变换、分数积分和导数算子下的像。 对应于这些多项式，我们定义了新型的双变量雅可比Konhauser梅塔格-莱弗勒（JKML）函数，并获得了它们的类似性质。