Differential-recurrence properties of dual Bernstein polynomials

TL;DR

This paper explores new differential and recurrence relations of dual Bernstein polynomials, linking them to Hahn and Jacobi polynomials, and derives a fourth-order differential equation and recurrence relation to enhance computational efficiency.

Contribution

It introduces novel differential-recurrence properties of dual Bernstein polynomials based on their relations with Hahn and Jacobi polynomials, including a new differential equation and recurrence relation.

Findings

Derived a fourth-order differential equation for dual Bernstein polynomials.

Established a fourth-order recurrence relation for these polynomials.

Linked dual Bernstein polynomials to Hahn and Jacobi polynomials.

Abstract

New differential-recurrence properties of dual Bernstein polynomials are given which follow from relations between dual Bernstein and orthogonal Hahn and Jacobi polynomials. Using these results, a fourth-order differential equation satisfied by dual Bernstein polynomials has been constructed. Also, a fourth-order recurrence relation for these polynomials has been obtained; this result may be useful in the efficient solution of some computational problems.