Applicability of the $q$-Analogue of Zeilberger's Algorithm

$q$-类比的Wilf-Zeilberger种子与Ramanujan $1/π^k$-公式

$q$-analogues of Wilf-Zeilberger seeds and Ramanujan $1/π^k$-formulas

本文提出Wilf-Zeilberger种子的概念，用于生成$q$-类比的Ramanujan型$1/π^k$公式，并揭示了部分非模形式的模伪模实例。

A simple proof of the Zeilberger-Bressoud q-Dyson theorem

As an application of the Combinatorial Nullstellensatz, we give a short polynomial proof of the q-analogue of Dyson's conjecture formulated by Andrews and first proved by Zeilberger and Bressoud.

The Extended Zeilberger's Algorithm with Parameters

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 problem concerning several similar hypergeometric terms $f_1(k, a, b,..., c)$, $f_2(k, a,b, ..., c)$, $...$, $f_m(k, a, b, ..., c)$. We present an algorithm to derive a linear relation among the sums $\sum_k f_i(k,a,b,...,c)$ $(1\leq i \leq m)$. Furthermore, when the summand $f_i$ contains the parameter $x$, we can require that the coefficients be $x$-free. Suc…

How to generate all possible rational Wilf-Zeilberger pairs?

A Wilf--Zeilberger pair $(F, G)$ in the discrete case satisfies the equation $ F(n+1, k) - F(n, k) = G(n, k+1) - G(n, k)$. We present a structural description of all possible rational Wilf--Zeilberger pairs and their continuous and mixed analogues.

应对 Ekhad 和 Zeilberger 提出的一个与 Stern 三角形相关的挑战

Meeting a Challenge raised by Ekhad and Zeilberger related to Stern's Triangle

针对与 Stern 三角形相关的 ω(10000) 计算难题，论文整合常数项、条件转移矩阵、代数生成函数与 P-递归，算出该 6591 位数值。

Nouvelles statistiques de partitions pour les q-nombres de Stirling de seconde espece

Steingrimsson has recently introduced a partition analogue of Foata-Zeilberger's mak statistic for permutations and conjectured that its generating function is equal to the classical q-Stirling numbers of second kind. In this paper we prove a generalization of Steingrimsson's conjecture.