Stable D-finite Functions Under Integration

2024-07-25

10:00 AM - 11:00 AM

MA205

Details

  • Time:10:00-11:00 pm (Beijing Time)
  • Date: Friday, 25th July, 2024
  • Venue: MA205
  • Speaker:Ruyong Feng (Academy of Mathematics and Systems Science, CAS)
  • Language: English

Abstract

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.

Speaker

Ruyong Feng received his PhD (Candidate of Sciences) from the Academy of Mathematics and Systems Science, CAS. He is currently a Professor at the Academy of Mathematics and Systems Science, CAS. His research interests include symbolic computation and differential/difference Galois theory. He improved Hrushovski’s algorithm for computing differential Galois groups, proved Matzat’s conjecture for absolutely differential Galois groups, and developed an algorithm to compute difference Galois groups.

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