Symmetric identities of Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a Dirichlet character \(\chi\) (Q2337849)

Summary: We aim to introduce arbitrary complex order Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a Dirichlet character \(\chi\) and investigate certain symmetric identities involving the polynomials, by mainly using the theory of \(p\)-adic integral on \(\mathbb{Z}_p\). The results presented here, being very general, are shown to reduce to yield symmetric identities for many relatively simple polynomials and numbers and some corresponding known symmetric identities.