Q-Differential Equations of Higher Order and Structural Properties of the Approximate Roots for q-Modified Derangements’ Polynomials

Abstract

The objective of this study is to find q-differential equations of higher order related to q-modified derangements’ polynomials and confirm the structure of approximation roots. Furthermore, it states several symmetric properties of q-differential equations of higher order and the special properties of the approximation roots of q-modified derangements’ polynomials.