Related papers: On an identity derived from interpolation theory
In this paper we present a new identity and some of its variants which can be used for finding solutions while solving fractional infinite and finite series. We introduce another simple identity which is capable of generating solutions for…
We give a first-order definition of key polynomials, we show the links with previous definitions, that it is relevant to study key degrees, and to use a kind of valuations that we call partially multiplicative. We also prove or reprove…
In this paper, we study properties of polynomials over division rings. Moreover, we present formulas for finding roots of some polynomials
In this paper, we derive basic identities of symmetry in two variables related to higher-order q-Euler polynomials and q-analogue of higher order alternating power sums. The derivation of identities are based on the multibvariate p-adic…
We develop a rather general approach to entanglement characterization based on convexity properties and polynomial identities. This approach is applied to obtain simple and efficient entanglement conditions which work equally well in both…
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
This article explains the similar appearance of two polynomial identities involving Dickson polynomials in char. 2, one found by Abhyankar, Cohen, and Zieve, and the other found by the author.
Let $A$ be a finite dimensional real algebra with a division grading by a finite abelian group $G$. In this paper we provide finite basis for the $T_G$-ideal of graded identities and for the $T_G$-space of graded central polynomials for…
We present a differential-calculus-based method which allows one to derive more identities from {\it any} given Fibonacci-Lucas identity containing a finite number of terms and having at least one free index. The method has two {\it…
We obtain identities involving symmetric and doubly symmetric polynomials. These identities provide a way of handling expressions appearing in the Atiyah-Bott-Berline-Vergne formula for Grassmannians. As corollaries, we obtain formulas for…
We consider a special class of binomial sums involving harmonic numbers and we prove three identities by using the elementary method of the partial fraction decomposition. Some applications to infinite series and congruences are given.
Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
We derive new identities involving zeros of the Bessel function $J_{\nu}$ and some related functions. These are special cases of more general identities obtained in this note, which might also be of interest.
We describe the T-ideal of identities and the T-space of central polynomials for the unitary finite dimensional Grassmann algebra over a finite field.
The aim of this note is to survey the factorizations of the Fibonacci infinite word that make use of the Fibonacci words and other related words, and to show that all these factorizations can be easily derived in sequence starting from…
We bring an abstract model theory perspective to interpolation. We ask, what is the role of interpolation in the study of extensions of first order logic, such as infinitary logics, generalized quantifiers and higher order logics? The…
In this brief semi-expository article we present a few efficient techniques for calculating and proving determinantal identities. Several stimulating examples of different flavor and applications are spread across the pages which we hope…
We compute the graded polynomial identities of the infinite dimensional upper triangular matrix algebra over an arbitrary field. If the grading group is finite, we prove that the set of graded polynomial identities admits a finite basis. We…
We naturally obtain some combinatorial identities finding the difference analogs of hyperbolic and trigonometric functions of order $n.$ In particular, we obtain the identities connected with the proved in the paper the addition formulas…