We propose a way to split a given bivariate P-recursive sequence into a summable part and a non-summable part in such a way that the non-summable part is minimal in some sense. This decomposition gives rise to a new reduction-based creative telescoping algorithm based on the concept of integral bases.

Publication:

Journal of Symbolic Computation, Volume 126, January–February 2025, 102341

http://dx.doi.org/10.1016/j.jsc.2024.102341

Author:

Shaoshi Chen

KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

Email: schen@amss.ac.cn

Lixin Du

Institute for Algebra, Johannes Kepler University, Linz, A4040, Austria

Manuel Kauers

Institute for Algebra, Johannes Kepler University, Linz, A4040, Austria

Rong-Hua Wang

School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China