Differential equations for Changhee polynomials and their applications

TL;DR

This paper explores differential equations related to Changhee polynomials, deriving new explicit formulas and identities that enhance understanding of these polynomials and their applications in mathematical physics.

Contribution

It introduces new differential equations for Changhee polynomials and derives explicit formulas and identities, expanding their theoretical framework.

Findings

New differential equations for Changhee polynomials

Explicit formulas and identities derived from these equations

Enhanced understanding of Changhee polynomials in mathematical physics

Abstract

Recently, the non-linear Changhee differential equations were introduced in [5] and these differential equations turned out to be very useful for studying special polynomials and mathematical physics. Some interesting identities and properties of Changhee polynomials can also be derived from umbral calculus (see [7]). In this paper, we consider differential equations arising from Changhee polynomials and derive some new and explicit formulae and identities from our differential equations.