A nonterminating 8φ7 summation for the root system Cr

Using multiple q-integrals and a determinant evaluation, we establish a nonterminating ₈φ₇ summation for the root system C_r. We also give some important specializations explicitly.     

一类q-级数恒等式的新证法

本文利用一个已知的变换公式及其它基本超几何函数的求和公式，给出了一类ｑ级数恒等式的新的更简单的证明，并建立了该类恒等式的一般形式．     

Note on the Monotonicity of Coefficients for Some q-Series Arising from Ramanujan's Lost Notebook

In this note, we shall give a partition-theoretic interpretation which explains the non-negativity of the coefficients of some q-series arising from Ramanujan's Lost Notebook and prove the almost-increasingness of the coefficients via a vector partition generating function.     

q-Laguerre polynomials and related q-partial differential equations

In this paper, we define two homogenous q-Laguerre polynomials, by introducing a modified q-differential operator, we prove that an analytic function can be expanded in terms of the q-Laguerre polynomials if and only if the function satisfies certain q-partial differential equations. Using this main result, we derive the generating functions, bilinear generating functions and mixed generating functions for the q-Laguerre polynomials and generalized q-Hahn polynomials. Cigler’s polynomials and its generating functions discussed in [J. Cao, D.-W. Niu, A note on q -difference equations for Cigler’s polynomials, J. Difference Equ. Appl. 22 (2016), 1880–1892.] are generalized. At last, we obtain an q-integral identity involving q-Laguerre polynomials. These applications indicate that the q-partial differential equation is an effective tool in studying q-Laguerre polynomials.     

Démonstration Élémentaire d'une Identité de Lorenz

We give an elementary proof of an identity due to L. Lorenz giving the number of representations of a positive integer by the quadratic form x2 + 2y2 using Jacobi's triple product identity.     

Duality for finite multiple harmonic q-series

We define two finite q-analogs of certain multiple harmonic series with an arbitrary number of free parameters, and prove identities for these q-analogs, expressing them in terms of multiply nested sums involving the Gaussian binomial coefficients. Special cases of these identities—for example, with all parameters equal to 1—have occurred in the literature. The special case with only one parameter reduces to an identity for the divisor generating function, which has received some attention in connection with problems in sorting theory. The general case can be viewed as a duality result, reminiscent of the duality relation for the ordinary multiple zeta function.     

A Higher Level Bailey Lemma: Proof and Application

In a recent letter, new representations were proposed for the pair of sequences (,), as defined formally by Bailey in his famous lemma. Here we extend and prove this result, providing pairs (,) labelled by the Lie algebra AN – 1, two nonnegative integers and k and a partition , whose parts do not exceed N – 1. Our results give rise to what we call a higher level Bailey lemma. As an application it is shown how this lemma can be applied to yield general q-series identities, which generalize some well-known results of Andrews and Bressoud.     

A few remarks on quadratic harnesses

We analyse and partially solve system of recurrences that can be derived from the properties of orthogonal martingale polynomials that characterize quadratic harnesses (QHs). We also specify conditions for the existence of moments of one dimensional distributions for large classes of QHs that are also Markov processes complementing earlier results.