Subresultants in multiple roots: an extremal case

TL;DR

This paper derives explicit hypergeometric formulas for the coefficients of subresultants of two polynomials with multiple roots, specifically in the extremal case where roots coincide, using determinants of binomial Hankel matrices.

Contribution

It introduces explicit formulas for subresultants of polynomials with multiple roots in the extremal case, expanding the understanding of polynomial resultants in this context.

Findings

Explicit hypergeometric formulas for subresultant coefficients.

Representation of formulas via determinants of binomial Hankel matrices.

Application to polynomials with multiple roots in extremal cases.

Abstract

We provide explicit formulae for the coefficients of the order-d polynomial subresultant of (x-\alpha)^m and (x-\beta)^n with respect to the set of Bernstein polynomials \{(x-\alpha)^j(x-\beta)^{d-j}, \, 0\le j\le d\}. They are given by hypergeometric expressions arising from determinants of binomial Hankel matrices.