From big q-Jacobi and Chebyshev polynomials to exponential-reproducing subdivision: new identities

TL;DR

This paper derives new identities for Chebyshev and big q-Jacobi polynomials, enabling closed-form expressions for subdivision schemes that reproduce exponential functions with minimal support.

Contribution

It introduces novel identities for these polynomials and applies them to develop efficient subdivision schemes reproducing exponential powers.

Findings

New identities for Chebyshev and big q-Jacobi polynomials

Closed-form expressions for exponential-reproducing subdivision schemes

Efficient minimal-support interpolation schemes

Abstract

In this paper we derive new identities satisfied by Chebyshev polynomials of the first kind and big q-Jacobi polynomials. An immediate benefit of the derived identities is the achievement of closed-form expressions for the Laurent polynomials that identify minimum-support interpolating subdivision schemes reproducing finite sets of integer powers of exponentials.