A Note on Degenerate Hermite Poly–bernoulli Numbers and Polynomials
نویسندگان
چکیده
In this paper, we introduce a new class of degenerate Hermite poly-Bernoulli polynomials and give some identities of these polynomials related to the Stirling numbers of the second kind. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions. These results extend some known summations and identities of degenerate Hermite poly-Bernoulli numbers and polynomials. Mathematics subject classification (2010): 11B68, 11B73, 11B83, 33C45.
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 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 کاملA Note on Partially Degenerate Bernoulli Numbers and Polynomials
In this paper, we consider the partially degenerate Bernoulli numbers and polynomials of the first kind and the second kind and investigate some properties of these numbers and polynomials.
متن کاملA Note on Extended Binomial Coefficients
We study the distribution of the extended binomial coefficients by deriving a complete asymptotic expansion with uniform error terms. We obtain the expansion from a local central limit theorem and we state all coefficients explicitly as sums of Hermite polynomials and Bernoulli numbers.
متن کاملOn composition of generating functions
In this work we study numbers and polynomials generated by two type of composition of generating functions and get their explicit formulae. Furthermore we state an improvementof the composita formulae's given in [6] and [3], using the new composita formula's we construct a variety of combinatorics identities. This study go alone to dene new family of generalized Bernoulli polynomials which incl...
متن کامل