Related papers: Explanation of a Polynomial Identity
We formulate several polynomial identities. One side of these identities has a nice simple form. Whereas the other has a form of a polynomial whose coefficients contain binomial coefficients double factorials or (and) rising factorials. The…
In this article we shows some results about algebra with the group of units having special polynomial identity.
In this paper, we first give a simple combinatorial proof of Tepper's identity. Then, as a by product of this interesting identity we present another proof of the well-known Wilson's identity in number theory. Finally, we obtain a…
The aim of this short note is to show how can be derived from the properties of fundamental interpolation polynomials some nice identities.
We give an elementary probabilistic proof of a binomial identity. The proof is obtained by computing the probability of a certain event in two different ways, yielding two different expressions for the same quantity.
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…
We propose and prove a new polynomial identity that implies Schur's partition theorem. We give combinatorial interpretations of some of our expressions in the spirit of Kur\c{s}ung\"oz. We also present some related polynomial and $q$-series…
We discuss an algebraic identity, due to Sylvester, as well as related algebraic identities and applications.
In most text books on number theory Wilson Theorem is proved by applying Lagrange theorem concerning polynomial congruences.Hardy and Wright also give a proof using cuadratic residues. In this article Wilson theorem is derived as a…
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…
We survey the area of algebraic complexity theory; with the focus being on the problem of polynomial identity testing (PIT). We discuss the key ideas that have gone into the results of the last few years.
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.
Given two combinatorial identities proved earlier, a new set of variations of these combinatorial identities is listed and proved with the integral representation method. Some identities from literature are shown to be special cases of…
We give explicit formulae and study the combinatorics of an identity holding in all Rota-Baxter algebras. We describe the specialization of this identity for a couple of examples of Rota-Baxter algebras.
In this paper, we study some properties of associated sequences of special polynomials. From the properties of associated sequences of polynomials, we derive some interesting identities of special polynomials.
This is a short review of some recent results obtained by the author. These results are related the problem of obtaining polynomial identities (computational formulas) for some matrix functions by means of the known polarization theorem,…
The Jacobi identity is one of the properties that are used to define the concept of Lie algebra and in this context is closely related to associativity. In this paper we provide a complete description of all bivariate polynomials that…
We derive an identity that relates a class of multiple integrals involving Vandermonde polynomials to divided differences. Alternatively the identity can be viewed as an integral formula for divided differences. As part of the derivation we…
In this papier, by the classical umbral calculus method, we establish identities involving the Appell polynomials and extend some existing identities.
We first establish the result that the Narayana polynomials can be represented as the integrals of the Legendre polynomials. Then we represent the Catalan numbers in terms of the Narayana polynomials by three different identities. We give…