Related papers: A new four parameter q-series identity and its par…

In 1991, the Borweins established a cubic analogue of Jacobi's identity for theta functions, which is used by B.C. Berndt, S. Bhargava, and F.G. Garvan in the development of Ramanujan's cubic theory of elliptic functions. In 2013, D.…

Resorting to the recursions satisfied by the polynomials which converge to the right hand sides of the Rogers-Ramanujan type identities given by Sills and a determinant method presented in a paper by Ismail-Prodinger-Stanton, we obtain many…

We present a Bayesian methodology for infinite as well as finite dimensional parameter identification for partial differential equation models. The Bayesian framework provides a rigorous mathematical framework for incorporating prior…

In our previous paper math.QA/0412192 the Cayley-Hamilton identity for the GL(m|n) type quantum matrix algebra was obtained. Here we continue investigation of that identity. We derive it in three alternative forms and, most importantly, we…

In this work, we construct a new Bailey pairs for the integral pentagon identity in terms of q-hypergeometric functions. The pentagon identity considered here represents equality of the partition functions of a certain three-dimensional…

In [14] we introduced a new class of algebras, which we named \textit{quantum generalized Heisenberg algebras} and which depend on a parameter $q$ and two polynomials $f,g$. We have shown that this class includes all generalized Heisenberg…

In the lecture notes we start off with an introduction to the $q$-hypergeometric series, or basic hypergeometric series, and we derive some elementary summation and transformation results. Then the $q$-hypergeometric difference equation is…

Motivated by the telescoping proofs of two identities of Andrews and Warnaar, we find that infinite q-shifted factorials can be incorporated into the implementation of the q-Zeilberger algorithm in the approach of Chen, Hou and Mu to prove…

The present paper proves a $q$-identity, which arises from a representation $\pi_{N,\psi}$ of $\text{GL}_n(\mathbb{F}_q)$. This identity gives a significant simplification for the dimension of $\pi_{N,\psi}$, which allowed the second author…

The Jacobi-Trudi formula implies some interesting quadratic identities for characters of representations of $gl_n$. Earlier work of Kirillov and Reshetikhin proposed a generalization of these identities to the other classical Lie algebras,…

In this paper, we derive basic identities of symmetry in two variables related to higher-order q-Euler polynomials and q-analogue of higher order alternating power sums. The derivation of identities are based on the multibvariate p-adic…

We study the Identity Problem, the problem of determining if a finitely generated semigroup of matrices contains the identity matrix; see Problem 3 (Chapter 10.3) in ``Unsolved Problems in Mathematical Systems and Control Theory'' by…

For a hypergeometric series $\sum_k f(k,a, b, ...,c)$ with parameters $a, b, >...,c$, Paule has found a variation of Zeilberger's algorithm to establish recurrence relations involving shifts on the parameters. We consider a more general…

$q$-Analogues of the coefficients of $x^a$ in the expansion of $\prod_{j=1}^N (1+x+...+x^j)^{L_j}$ are proposed. Useful properties, such as recursion relations, symmetries and limiting theorems of the ``$q$-supernomial coefficients'' are…

We present several identities with a form of polynomials or rational functions that involve Pochhammer and q-Pochhammer symbols and q-binomials (i.e. Gauss polynomials). All these identities were obtained by some analytical methods based on…

Let $p$ be an odd prime and $q=p^r$, $r\geq 1$. For positive integers $n$, let ${_n}G_n[\cdots]_q$ denote McCarthy's $p$-adic hypergeometric functions. In this article, we prove an identity expressing a ${_4}G_4[\cdots]_q$ hypergeometric…

We determine an infinite family of linear identities for the number $A_4(n)$ of partition pairs of $n$ with $4$-cores by employing elementary $q$-series techniques and certain $3$-dissection formulas. We then discover an infinite family of…

We obtain a three-parameter $q$-series identity that generalizes two results of Chan and Mao. By specializing our identity, we derive new results of combinatorial significance in connection with $N(r, s, m, n)$, a function counting certain…

In this paper we generalize the famous Jacobi's triple product identity, considered as an identity for theta functions with characteristics and their derivatives, to higher genus/dimension. By applying the results and methods developed in…

Recently Andrews and Bachraoui proved identities relating certain restricted partitions into distinct even parts with restricted 4-regular partitions by the theory of basic hypergeometric series. They also posed a question regarding…