# On certain polynomial systems involving Stirling numbers of second kind

## TL;DR

This paper addresses solving specific polynomial systems involving Stirling numbers, which are crucial for computing parametric Bernstein-Sato polynomials related to hypergeometric ideals in the Weyl algebra.

## Contribution

It introduces methods for solving particular polynomial systems with Stirling numbers, advancing the computation of Bernstein-Sato polynomials in algebraic analysis.

## Key findings

- Established solutions for special polynomial systems with Stirling numbers.
- Applied solutions to compute parametric Bernstein-Sato polynomials.
- Connected polynomial systems to hypergeometric ideals in the Weyl algebra.

## Abstract

We solve a special type of linear systems with coefficients in multivariate polynomial rings. These systems arise in the computation of parametric Bernstein-Sato polynomials associated with certain hypergeometric ideals in the Weyl algebra.