Related papers: A Generalized Newton-Girard Identity

In this note, we show how a combinatorial identity of Frisch can be applied to prove and generalize some well-known identities involving harmonic numbers. We also present some combinatorial identities involving odd harmonic numbers which…

In this paper we derive some interesting identities arising from the orhtogonality of gegenbauer polynomials.

In this paper, we establish some formulas for the noncentral Tanny-Dowling polynomials including sums of products and explicit formulas which are shown to be generalizations of known identities. Other important results and consequences are…

Binomial versions of the Andrews-Gordon-Bressoud identities are given.

Foster's network theorems and their extensions to higher orders involve resistance values and conductances. We establish identities concerning voltage values and conductances. Our identities are analogous to the extended Foster's…

We study a generalization of the classical Pentagonal Number Theorem and its applications. We derive new identities for certain infinite series, recurrence relations and convolution sums for certain restricted partitions and divisor sums.…

For the Schur polynomials bounded and unbounded generalizations of the Cauchy identities are found.

Starting with a known polynomial identity, we derive two generalizations of Touchard's identity concerning Catalan numbers; one obtained using the Beta function and the other via a connection with Stirling numbers of the second kind. We…

In this note, we provide a conceptual explanation of a well-known polynomial identity used in algebraic number theory.

Some applications of a result, which is proved recently, is considered. We first prove three determinantal identities concerning the binomial coefficient and Stirling numbers of the first and the second kind. We also easily obtain the…

In this paper we give new identities involving q-Euler polynomials of higher order.

Some identities of Chebyshev polynomials are deduced from Waring's formula on symmetric functions. In particular, these formulae generalize some recent results of Grabner and Prodinger.

We present other proofs, generalizations and analogues of the identities concerning multiple Dirichlet series by Tahmi and Derbal (2022). As applications, we obtain asymptotic formulas with remainder terms for certain related sums.

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

We first prove an identity involving symmetric polynomials. This identity leads us into exploring the geometry of Lagrangian Grassmannians. As an insight applications, we obtain a formula for the integral over the Lagrangian Grassmannian of…

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…

Tensor polynomial identities generalize the concept of polynomial identities on $d \times d$ matrices to identities on tensor product spaces. Here we completely characterize a certain class of tensor polynomial identities in terms of their…

A generalization of the Chu-Vandermonde convolution is presented and proved with the integral representation method. This identity can be transformed into another identity, which has as special cases two known identities. Another identity…

The Rogers-Ramanujan identities have been studied from the viewpoints of combinatorics, number theory, affine Lie algebras, statistical mechanics, and quantum field theory. This note connects the Rogers-Ramanujan identities with the finite…

In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.