Related papers: Comment on `A general integral identity'

In investigating the properties of a certain class of homogeneous polynomials, we discovered an identity satisfied by their coefficients which involves simple 2F1 Gauss hypergeometric functions. This result appears to be new and we supply a…

In this note, we use a basic identity, derived from the generalized doubling integrals of \cite{C-F-G-K1}, in order to explain the existence of various global Rankin-Selberg integrals for certain $L$-functions. To derive these global…

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.

In this article we prove a new elliptic hypergeometric integral identity. It previously appeared (as a conjecture) in articles by Rains, and Spiridonov and Vartanov. Moreover it gives a different proof of an identity in another article by…

We give a combinatorial proof of Guo's multi-generalization of Munarini's identity, answering a question of Guo.

We prove some new retarded integral inequalities. The results generalize those in [J. Math. Anal. Appl. 301 (2005), no. 2, 265--275].

We give three elementary proofs of a nice equality of definite integrals, which arises from the theory of bivariate hypergeometric functions, and has connections with irrationality proofs in number theory. We furthermore provide a…

The aim of this short note is to show how can be derived from the properties of fundamental interpolation polynomials some nice identities.

On the basis of the generalizations of the Jacobi identity found by the author some identities satisfied by the curvature and torsion of a covariant differentiation are derived. A kind of the generalized covariant differentiation is…

We present a generalization of the Newton-Girard identities, along with some applications. As an addendum, we collect many evaluations of symmetric polynomials to which these identities apply.

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.

Some generalized multi-sum Chu-Vandermonde identities are presented and proved, generalizing some known multi-sum Chu-Vandermonde identities from literature and adding some quadratic and cubic examples of these identities. Some other…

In 2002 Zhi-Wei Sun [Integers 2(2002)] published a curious identity involving binomial coefficients. In this paper we present a generalization of the identity.

In a recent paper, Caracciolo, Sokal and Sportiello presented, inter alia, an algebraic/combinatorial proof for Cayley's identity. The purpose of the present paper is to give a "purely combinatorial" proof for this identity; i.e., a proof…

We present a new and useful congruence identity satisfied by m-permutable varieties.

We prove an identity about partitions with a very elementary formulation. We had previously conjectured this identity, encountered in the study of shifted Jack polynomials (math.CO/9901040). The proof given is using a trivariate generating…

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

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

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 prove a new general differential identity and an associated integral identity, which entails a pair of solutions of the Poisson equation with constant source term. This generalizes a formula that the first and third authors previously…