A proof of a conjecture about a symmetric system of orthogonal polynomials

ABSTRACT

The purpose of this note is to give an affirmative answer to a conjecture appearing in Berg [Open problems. Integral Transforms Spec Funct. 2015;26(2):90–95].

KEYWORDS:

• Orthogonal polynomials
• symmetric system of orthogonal polynomials
• polynomial mappings

AMS CLASSIFICATIONS:

• 42C05
• 33C45

Acknowledgments

The authors thank the reviewer for the careful reading of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

KC and JP are supported by the Centre for Mathematics of the University of Coimbra–UID/MAT/00324/2019, funded by the Portuguese Government through FCT/MEC and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020. MNJ supported by UID/Multi/04016/2019, funded by Fundação para a Ciência e a Tecnologia (FCT). MNJ also thanks the Instituto Politécnico de Viseu and CI&DETS for their support.