Approximate Roots and Properties of Differential Equations for Degenerate q-Special Polynomials - Jung-Yoog Kang; Cheon-Seoung Ryoo (Mathematics, 2023)
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 <semantics>(q,h)</semantics>-differential equations for DQE polynomials and find some relations of q-differential and h-differential equations. By varying the values of <semantics>q,η</semantics>, and h, we observe the values of DQE numbers and approximate roots of DQE polynomials to obtain some properties and conjectures.