相关论文: Two Extensions of the Sury's Identity

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

In this note, we present several identities involving binomial coefficients and the two kind of Stirling numbers.

We present a list of equivalent expressions and extensions of Bougerol's celebrated identity in law, obtained by several authors. We recall well-known results and the latest progress of the research associated with this celebrated identity…

In this note, we will give a short proof of an identity for cubic partitions.

We prove several extensions of the Erdos-Fuchs theorem.

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

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

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

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…

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.

Sury's 2014 proof of an identity for Fibonacci and Lucas numbers (Identity 236 of Benjamin and Quinn's 2003 book: {\em Proofs that count: The art of combinatorial proof}) has excited a lot of comment. We give an alternate, telescoping,…

We prove some extensions of Andrews inequality.

We prove a conjecture that arose in the context of a subspace enumeration problem over finite fields. We prove, more generally, a bibasic, double-sum identity, which extends a $q$-analogue of the (terminating) binomial theorem.

A family of general integral identities is derived and several applications of physical interest are presented

We prove a curious identity for the Bernoulli numbers.

We provide bijective proofs of two classic identities that are very simple to prove using generating functions, but surprisingly difficult to prove combinatorially. The problem of finding a bijective proof for the first identity was first…

The main objective of this research note is to provide an identity for the H-function, which generalizes two identities involving H-function obtained earlier by Rathie and Rathie et al.

We show that a binomial identity arising in the context of the study of series expansions of $1/\pi$ can be seen as an incarnation of Whipples second theorem for hypergeometric series.

We obtain a finite form of Jacobi's identity and present a combinatorial proof based on the structure of synchronized partitions.

In this paper we establish two symmetric identities on sums of products of Euler polynomials.