The symbolic approach to study the family of Appell-$\lambda$ matrix polynomials

Abstract

In this research article, we introduced certain hybrid and matrix special polynomial associated
to lambda polynomials and established their properties. Further, the monomiality principle and dierential
equations for these newly introduced hybrid special polynomials are obtained. Also, we derive several
intrinsic outcomes for the special cases of these polynomials. Some examples for the members belonging
to the Appell-lambda associated families are considered. Next, the determinantal representations of the special
matrix polynomials and hybrid special polynomials associated with Appell-lambda polynomials are obtained.
The proposed approach in this article is symbolic. The Bernoulli-lambda numbers and Euler-lambda numbers are
also obtained. The graphical representations are also given as concluding remarks