Related papers: q-identities of Fu and Lascoux proved by the q-Ric…
We give a survey of some known and some new results about factors of different sorts of $q-$Fibonacci numbers.
We prove a curious identity for the Bernoulli numbers.
The q-binomial formula in the limit q->1 is shown to be equivalent to the Rogers five term dilogarithm identity.
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…
The relation of crystal bases with $q$-identities is discussed, and some new results on crystals and $q$-identities associated with the affine Lie algebra $C_n^{(1)}$ are presented.
We propose and prove a new polynomial identity that implies Schur's partition theorem. We give combinatorial interpretations of some of our expressions in the spirit of Kur\c{s}ung\"oz. We also present some related polynomial and $q$-series…
Combining Newton and Lagrange interpolation, we give $q$-identities which generalize results of Van Hamme, Uchimura, Dilcher and Prodinger.
Recently, Andrews and El Bachraoui (2024) proved three very interesting $q$-series identities, from which three simple looking identities involving certain restricted partitions into distinct even parts and $4$-regular partitions follow. In…
We give generalizations of a finite version of Euler's pentagonal number theorem and of a q-identity of Gauss.
The method of rational function certification for proving terminating hypergeometric identities is extended from single sums or integrals to multi-integral/sums and ``$q$'' integral/sums.
Applying the theory of elliptic functions we establish two Jacobi theta function identities. From these identities we confirm two q-trigonometric identities conjectured by Gosper. As an application, we give a new and simple proof of a…
In this paper we will prove a series of $q$-identities suggested by the realisation of certain conformal field theories by so-called `coupled free fermions'. We will consider $q$-series arising from coupled free fermions constructed by the…
We examine four identities conjectured by Hickerson which complement five modulo $9$ Kanade--Russell identities, and we build up a profile of new identities and new conjectures not unlike those found by Uncu and Zudilin.
We prove a partition identity conjectured by Lassalle (Adv. in Appl. Math. 21 (1998), 457-472).
In the process of studying a conjecture of Holly M. Green and Martin W. Liebeck, we obtain two interesting identities by elementary methods, one is a combinatorial identity, and the other is a number theoretic identity.
A simple heuristic proof of an integral identity recently derived (Glasser ML 2011 J. Phys. A: Math. Theor. 44 225202) is presented.
We explain the notion of "$q$-deformed real numbers" introduced in our previous work and overview their main properties. We will also introduce $q$-deformed Conway-Coxeter friezes.
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…
In this paper, by the technique of inverse relations and comparing coefficients, we establish some generalized forms of Andrews' q-series identity and two new Bailey pairs and q-identities closely related to Andrews-Warnaar's sum identity…
A. Lacasse conjectured a combinatorial identity in his study of learning theory. Various people found independent proofs. Here is another one that is based on the study of the tree function, with links to Lamberts $W$-function and…