相关论文: More on the identity of Chaundy and Bullard

The identity by Chaundy and Bullard expresses $1$ as a sum of two truncated binomial series in one variable where the truncations depend on two different non-negative integers. We present basic and elliptic extensions of the…

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 this paper, based on the WZ theory, a very succinct new proof, of an identity by Chaundy and Bullard, was given.

An identity by Chaundy and Bullard writes 1/(1-x)^n (n=1,2,...) as a sum of two truncated binomial series. This identity was rediscovered many times. Notably, a special case was rediscovered by I. Daubechies, while she was setting up the…

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…

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…

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

We consider two different interpretations of the Chu--Vandermonde identity: as an identity for polynomials, and as an identity for infinite matrices. Each interpretation leads to a class of possible generalizations, and in both cases we…

In this paper we prove some combinatorial identities which can be considered as generalizations and variations of remarkable Chu-Vandermonde identity. These identities are proved by using an elementary combinatorial-probabilistic approach…

We present some identities dealing with reflexive and admissible relations and which, through a variety, are equivalent to congruence modularity.

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 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…

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…

We first give a bijective proof of Gould's identity in the model of binary words. Then we deduce Rothe's identity from Gould's identity again by a bijection, which also leads to a double-sum extension of the $q$-Chu-Vandermonde formula.

In this paper, we study some properties of associated sequaences in umbral calculus. From these properties, we derive new and interesting identities of several kinds of polynomials.

We lift to the multivariate Eulerian polynomials the identity implying that univariate Eulerian polynomials are palindromic. As a consequence of this generalization, we obtain nice combinatorial identities that can be directly extracted…

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

We exhibit an identity that plays the same role as Vaughan's identity but is arguably simpler

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.

The article is a continuation of the author's work "Linear quasigroups. I" and devoted to linear quasigroups and some of their generalizations. In the second part identities and linearity of quasigroups are investigated, in particular, the…