Related papers: An alternative to Vaughan's identity

We establish a simple identity and using it we find a new proof of a result of Kloosterman.

We present a new twist on an old identity.

A simple proof of the higher Capelli identities is given.

We present and prove a general form of Vandermonde's identity and use it as an alternative solution to a classic probability problem.

We present an identity which can be regarded as a Pfaffian-Hafnian analogue of Borchardt's identity and as a generalization of Schur's identity. We give a proof using the complex analysis.

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 discuss an algebraic identity, due to Sylvester, as well as related algebraic identities and applications.

In this note we prove two extensions of the Sury's identity.

In this article, a short combinatorial proof of the Capelli's identity is given. It also leads to an easy proof of the Capelli--Cauchy--Binet identity, a more general form of Capelli's identity. With the technique introduced, the Turnbull's…

Some ramifications of the identity of Chaundy and Bullard are presented. We discuss its homogeneous form and its relations to other identities, as well as extensions to more variables and more parameters.

We study two identities involving roots of unity and determinants of Hermitian matrices which have been recently proved by using the famous eigenvector-eigenvalue identity for normal matrices. In this paper, we extend these identities to a…

We derive a new Fibonacci identity. This single identity subsumes important known identities such as those of Catalan, Ruggles, Halton and others, as well as standard general identities found in the books by Vajda, Koshy and others. We also…

We derive an identity involving Horadam numbers. Numerous new identities as well as those found in the existing literature are subsumed in this single identity.

We present a broader framework for the Cauchy identity derived from the determinant expansion of collocation matrices. This approach yields an infinite family of identities, where the original Cauchy identity stands as a particular case. To…

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…

In this paper, we give a short proof of a relation generalizing many identities for Bernoulli numbers.

An algebraical background of the Lattice Conformal Field Theory is refined with the help of a novel $q$-exponential identity.

We give a new proof of the existence of designs, which is much shorter and gives better bounds.

We give alternative proof of Melham's and Howard's identities on generalised Fibonacci numbers

Recently the second named author discovered a combinatorial identity in the context of vertex representations of quantum Kac-Moody algebras. We give a direct and elementary proof of this identity. Our method is to show a related identity of…