Properties of Differential Equations Related to Degenerate <i>q</i>-Tangent Numbers and Polynomials

Abstract

In this paper, we construct degenerate q-tangent numbers and polynomials and determine their related properties. Based on these numbers and polynomials, we also confirm that the structure of the approximate root changes according to changes in q and h. We find differential equations that have degenerate q-tangent polynomials as solutions and also find differential equations that have other polynomials as coefficients, confirming the relationships among these.

Keywords

• <i>q</i>-number
• (<i>q</i>, <i>h</i>)-derivative
• degenerate <i>q</i>-tangent polynomials
• differential equation