arXiv subjects

Xiuyun Li

Publications and source records attributed to Xiuyun Li.

3 recordsLinked to original sources

arXiv2026

Symbolic Integration in Weierstrass-like Extensions

This paper studies the integration problem in differential fields that may involve quantities reminiscent of the Weierstrass $\wp$ function, which are defined by a first-order nonlinear differential equation. We extend the classical notion of special polynomials to elements of Weierstrass-like extensions and present algorithms for reduction in such extensions. As an application of these results, we derive some new formulae for integrals of powers of $\wp$.

cs.SC↗

arXiv2025

Non-minimality of minimal telescopers explained by residues

Elaborating on an approach recently proposed by Mark van Hoeij, we continue to investigate why creative telescoping occasionally fails to find the minimal-order annihilating operator of a given definite sum or integral. We offer an explanation based on the consideration of residues.

cs.SC↗

arXiv2024

Parallel Summation in P-Recursive Extensions

We propose investigating a summation analog of the paradigm for parallel integration. We make some first steps towards an indefinite summation method applicable to summands that rationally depend on the summation index and a P-recursive sequence and its shifts. There is a distinction between so-called normal and so-called special polynomials. Under the assumption that the corresponding difference field has no unnatural constants, we are able to predict the normal polynomials appearing in the denominator of a potential closed form. We can also handle the numerator. Our method is incomplete so far as we cannot predict the special polynomials appearing in the denominator. However, we do have some structural results about special polynomials for the setting under consideration.

math.CO↗