New Insights into Bivariate Gauss‐Appell Polynomials with Application

ABSTRACT This paper presents various characterizations of the bivariate Gauss‐Appell polynomials, including their explicit forms, recurrence relations, determinant structure, and integral representation. Subsequently, the bivariate Gauss‐Bernoulli, Gauss‐Euler, and Gauss‐Hermite polynomials are introduced and their corresponding properties are established. Surface plots of these polynomials are also drawn. In the latter part of the study, an application is provided by constructing approximation operators in terms of the bivariate Gauss‐Appell polynomials to approximate functions defined over a semi‐infinite interval within a weighted function space. Additionally, a numerical example is given to demonstrate the convergence efficiency of the proposed operators.