TY - JOUR T1 - Higher Order Degenerate Hermite-Bernoulli Polynomials Arising from $p$-Adic Integrals on $mathbb{Z}_p$ TT - JF - IJMSI JO - IJMSI VL - 17 IS - 2 UR - http://ijmsi.ir/article-1-1455-en.html Y1 - 2022 SP - 171 EP - 189 KW - Multivariate $p$-adic invariant integral on $mathbb{Z}_p$ KW - Degenerate Bernoulli polynomials KW - Hermite polynomials. N2 - Our principal interest in this paper is to study higher order degenerate Hermite-Bernoulli polynomials arising from multivariate $p$-adic invariant integrals on $mathbb{Z}_p$. We give interesting identities and properties of these polynomials that are derived using the generating functions and $p$-adic integral equations. Several familiar and new results are shown to follow as special cases. Some symmetry identities are also established. M3 10.52547/ijmsi.17.2.171 ER -