Differential equations for Changhee polynomials and their applications

Recently, the non-linear Changhee differential equations were introduced by Kim and Kim [T. Kim, D. S. Kim, Russ. J. Math. Phys., 23 (2016), 1-5] 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 [D. S. Kim, T. Kim, J. J. Seo, Adv. Studies Theor. Phys., 7 (2013), 993-1003]). In this paper, we consider differential equations arising from Changhee polynomials and derive some new and explicit formulae and identities from our differential equations.