On the degrees of irreducible factors of higher order Bernoulli polynomials
نویسندگان
چکیده
1. Introduction. In this paper, we generalize the current results on the p-Eisenstein behavior of first and higher order Bernoulli polynomials [4], [6–9], using the machinery of [1]. In so doing, we provide a broader framework for the known results, all of which are either immediate consequences or special cases of our more general results. Because of an explicit formula for the coefficients in terms of falling factorials established in [1], the polynomials A n (x, −k) which we consider here are actually translates of the standard higher order Bernoulli polynomials B
منابع مشابه
Higher Order Degenerate Hermite-Bernoulli Polynomials Arising from $p$-Adic Integrals on $mathbb{Z}_p$
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. So...
متن کاملBernoulli matrix approach for matrix differential models of first-order
The current paper contributes a novel framework for solving a class of linear matrix differential equations. To do so, the operational matrix of the derivative based on the shifted Bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. An error estimation of presented method is provided. Numerical experiments are...
متن کاملModified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($alpha ,beta $)
The main goal of the present paper is to construct some families of the Carlitz's $q$-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz's $q$-Bernoulli polynomials and numbers with weight ($_{p}$. We then define the modified degenerate Carlitz's $q$-Bernoulli polynomials and numbers with weight ($alpha ,beta $) and obtain some recurrence relations and other identities...
متن کاملNumerical solution of a class of nonlinear two-dimensional integral equations using Bernoulli polynomials
In this study, the Bernoulli polynomials are used to obtain an approximate solution of a class of nonlinear two-dimensional integral equations. To this aim, the operational matrices of integration and the product for Bernoulli polynomials are derived and utilized to reduce the considered problem to a system of nonlinear algebraic equations. Some examples are presented to illustrate the efficien...
متن کامل