Speaker:    黄辉  副教授 (大连理工大学)

Inviter:      陈绍示（中国科学院数学机械化重点实验室）

Title:          Karr's Theory of Summation in Finite Terms I, II, III, IV

Time & Venue:  

2023年9月7日周四下午 15:00-16:00，思源楼525 

2023年9月9日周六下午 15:00-16:00，思源楼525 

2023年9月12日周二下午 15:00-16:00，思源楼525 

2023年9月14日周四下午 15:00-16:00，思源楼525 

摘要： A fundamental problem in symbolic summation is determining, within a finite number of steps, whether a given sum can be expressed in closed form and, if possible, computing such a form. This problem is known as the problem of summation in finite terms. In 1978, Gosper successfully solved this problem for hypergeometric terms. In 1981, Karr, utilizing the theory of difference fields, extended Gosper's algorithm to address more involved classes of special functions, including holonomic functions.  Karr's algorithm can be seen as the summation counterpart of Risch's algorithm for indefinite integration, and holds significant importance in symbolic summation. In this series of talks, we are going to thoroughly examine this celebrated algorithm. If time permits, we will also discuss potential topics for future research.

报告人简介： 黄辉，大连理工大学副教授，主要研究兴趣包括计算机代数、符号求和与符号积分、微分与差分代数、符号渐进分析等，以及这些在组合数学和其他领域中的交叉应用。