报告名称： Stable D-finite Functions Under Integration

报告专家：冯如勇

专家所在单位：中国科学院数学与系统科学研究院

报告时间：2025-06-09，下午15:30-16:30点

报告地点: 数统楼203

专家简介：

冯如勇，中国科学院数学与系统科学研究院研究员，2005年在中国科学院数学与系统科学研究院获得博士学位。主要研究方向为：符号计算，微分/差分代数，发展了非线性自治微分差分方程的符号求解算法，改进了Hrushovski计算微分伽罗瓦群的算法、证明了关于绝对微分伽罗瓦群的Matzat猜想，并开发了计算差分伽罗瓦群的算法。于2010年获得中科院系统科学研究所关肇直青年研究奖、2014年获得中科院数学与系统科学研究院突出科研成果奖，2017年获得首届吴文俊计算机数学青年学者奖，2021年获得国际符号与代数计算年会最佳论文奖。

报告摘要：

The problem of integration in finite terms is a classical topic in analysis, dating back to the times of Abel and Liouville. In the 1940s, Ritt introduced a new algebraic technique to tackle this problem, and these algebraic ideas have been further developed by many researchers since then. In this talk, we will focus on the conditions under which a given function is stable under integration, i.e., the iterated indefinite integrals of this function can be expressed as linear combinations of the function itself and its derivatives. We have proven that every D-finite function is eventually stable under integration, meaning that after a finite number of integrations, it becomes stable. Furthermore, we have described the structure of stable hyperexponential functions. This talk is based on joint work with Shaoshi Chen, Zewang Guo and Wei Lu.