Guozhu Ruan | Searcharxiv

arXiv2024

Multidimensional Rogers-Ramanujan type identities with parameters

Via the contour integral method, we establish a reduction formula from a double series to a single series with parameters, which not only implies Uncu and Zudilin's two results and Cao and Wang's two results, but also is related to Berkovich and Warnaar's equation. Similarly, we also discover some triple-sum generalizations of Cao and Wang's formulas. As conclusions, several multidimensional Rogers--Ramanujan type identities with parameters or without parameters are given.

math.CO↗

arXiv2022

Double series for $π$ and their $q$-analogues

With the help of the partial derivative operator and several summation formulas for hypergeometric series, we find three double series for $π$. In terms of the operator just stated and several summation formulas for basic hypergeometric series, we also establish $q$-analogues of these double series.

math.CO↗