Approximate Roots and Properties of Differential Equations for Degenerate q-Special Polynomials

Abstract

In this paper, we generate new degenerate quantum Euler polynomials (DQE polynomials), which are related to both degenerate Euler polynomials and q-Euler polynomials. We obtain several (q,h)-differential equations for DQE polynomials and find some relations of q-differential and h-differential equations. By varying the values of q,η, and h, we observe the values of DQE numbers and approximate roots of DQE polynomials to obtain some properties and conjectures.