Two applications of the Gosper algorithm

主講人：穆彥平 天津理工大學(xué)教授

時(shí)間：2024年7月11日15：30

地點(diǎn)：三號(hào)樓332室

舉辦單位：數(shù)理學(xué)院

主講人介紹：穆彥平，天津理工大學(xué)教授，2006年博士畢業(yè)于南開(kāi)大學(xué)，主要的研究方向是符號(hào)計(jì)算，在Journal of Symbolic Computation, The Ramanujan Journal, Journal of Number Theory等雜志上發(fā)表多篇論文。

內(nèi)容介紹：Firstly, we present a method for constructing simple Bailey pairs based on the q-Gosper algorithm. We illustrate this method by determining Gosper-summable q-hypergeometric terms with specific forms. As applications, we derive some summation and transformation formulas for q-series. Secondly, we utilize the extended Zeilberger algorithm to construct WZ (Wilf-Zeilberger) pairs. To illustrate the process, we start with identity (H.1) as provided by Van Hamme. We find eleven WZ pairs. Using these WZ pairs, we derive various summation formulas, transformation formulas, and supercongruences. Additionally, we present a strategy for constructing q-WZ pairs from WZ pairs and provide two q-analogues of (H.1).