Related papers: A master identity for Horadam numbers
We prove a double binomial sum identity which differs from most binomial sum identities in that the summands involve the absolute value function. The identity is of interest because it can be used in proofs of lower bounds for the Hadamard…
We give a new proof of a polynomial identity involving the minors of a matrix, that originated in the study of integer torsion in a local cohomology module.
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 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.
In this article, we will discover some new generalized identity regarding continued fractions. We will connect the results to Fibonacci numbers and Lucas numbers. For all the proof, we will use induction.
We prove a curious identity for the Bernoulli numbers.
By investigating a recurrence relation about functions, we first give alternative proofs of various identities on Fibonacci numbers and Lucas numbers, and then, make certain well known identities visible via certain trivalent graph…
Using elementary means, we prove several identities involving the M\"obius function, generalizing in the multidimensional case well-known formulas coming from convolution arguments.
We present new proofs of two identities arising in the work of Mourad Ismail using partition theoretic generating function interpretations.
We exhibit an identity that plays the same role as Vaughan's identity but is arguably simpler
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.
In this note we present a method for obtaining a wide class of combinatorial identities. We give several examples, in particular, based on the Gamma and Beta functions. Some of them have already been considered by previously, and other are…
In this article, we use the Touchard identity in order to obtain new integral representations for Catalan numbers. The main idea consists in combining the identity with a known integral representation and resorting to the binomial theorem.…
All the already known results on self descriptive numbers, together with the demonstration of the uniqueness for bases greater than 6, are here obtained through a systematic scheme of proof and not trial and error. The proof is also…
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…
We derive several identities that feature irreducible characters of the general linear, the symplectic, the orthogonal, and the special orthogonal groups. All the identities feature characters that are indexed by shapes that are "nearly"…
This purpose of this paper is to note an interesting identity derived from an integral in Gradshteyn and Ryzhik using techniques from George Boros'(deceased) Ph.D thesis. The idenity equates a sum to a product by evaluating an integral in…
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…
In this paper, we give a short proof of a relation generalizing many identities for Bernoulli numbers.
Several new identities for elliptic hypergeometric series are proved. Remarkably, some of these are elliptic analogues of identities for basic hypergeometric series that are balanced but not very-well-poised.