Related papers: Some identities involving Gegenbauer polynomials
In this papier, by the classical umbral calculus method, we establish identities involving the Appell polynomials and extend some existing identities.
In this paper, we consider the degenerate Frobenius-Euler polynomials and investigate some identities of these polynomials.
The purpose of this paper is to present a syatemic study of some familes of higher-order Euler numbers and polynomials. In particular, by using the basis property of higher-order Euler polynomials for the space of polynomials of degree less…
Our paper deals about identities involving Bell polynomials. Some identities on Bell polynomials derived using generating function and successive derivatives of binomial type sequences. We give some relations between Bell polynomials and…
In this paper, we study the Carlitz's degenerate Bernoulli numbers and polynomials and give some formulae and identities related to those numbers and polynomials.
In the paper we provide some polynomial identities for finite-dimensional algebras. A list of well known single polynomial identities is exposed and the classification of all $2$-dimensional algebras with respect to these identities is…
In this paper, we consider various speical mixed-type polynomials which are related to Bernoulli, Euler, Changhee and Daehee polynomials. From those polynomials, we derive some interesting and new identities
The purpose of this paper is to give some new identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials.
In this paper, we prove new identities for Bernoulli polynomials that extend Alzer and Kwong's results. The key idea is to use the Volkenborn integral over $\mathbb Z_p$ of the Bernoulli polynomials to establish recurrence relations on the…
In this paper, we study umbral calculus to have alternative ways of obtaining our results. That is, we derive some interesting identities of the higher-order Bernoulli, Euler and Hermite polynomials arising from umbral calculus to have…
New convolution identities of hypergeometric Bernoulli polynomials are presented. Two different approaches to proving these identities are discussed, corresponding to the two equivalent definitions of hypergeometric Bernoulli polynomials as…
In this paper, we give some interesting identities of higher-order Bernoulli, Frobenius-Euler and Euler polynomials arising from umbral calculus. From our method of this paper, we can derive many interesting identities of special…
We identify the Atkin polynomials in terms of associated Jacobi polynomials. Our identificationthen takes advantage of the theory of orthogonal polynomials and their asymptotics to establish many new properties of the Atkin polynomials.…
In this paper, we study linear differential equations arising from Bessel polynomials and their applications. From these linear differential equations, we give some new and explicit identities for Bessel polynomials.
We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…
For the Schur polynomials bounded and unbounded generalizations of the Cauchy identities are found.
In this paper, we introduce a novel identity for generalized Euler polynomials, leading to further generalizations for several relations involving classical Euler numbers, Euler polynomials, Genocchi polynomials, and Genocchi numbers.
We lift to the multivariate Eulerian polynomials the identity implying that univariate Eulerian polynomials are palindromic. As a consequence of this generalization, we obtain nice combinatorial identities that can be directly extracted…
In this paper, we establish an identity for Bernoulli's generalized polynomials. We deduce generalizations for many relations involving classical Bernoulli numbers or polynomials. In particular, we generalize a recent Gessel identity.
In this paper, we study nonlinear differential equations arising from Eulerian polynomials and their applications. From our study of nonlinear differential equations, we derive some new and explicit identities involving Eulerian and…