A parametric type of Bernoulli polynomials with higher level

Abstract

In this paper, we introduce a parametric type of Bernoulli polynomials with higher level and study their characteristic and combinatorial properties. We also give determinant expressions of a parametric type of Bernoulli polynomials with higher level. The results are generalizations of those with level 2 by Masjed-Jamei, Beyki and Koepf and with level 3 by the author.