# Solution of an Open Problem about Two Families of Orthogonal Polynomials

## TL;DR

This paper solves an open problem by identifying one family of orthogonal polynomials as Wilson polynomials and characterizes the other as a new discrete orthogonal family with specific asymptotic properties.

## Contribution

It identifies one of two new polynomial families as Wilson polynomials and introduces the other as a novel discrete orthogonal family with detailed asymptotic analysis.

## Key findings

- Identified one polynomial family as Wilson polynomials.
- Characterized the second family as a new discrete orthogonal family.
- Provided asymptotic behavior of the second family as degree increases.

## Abstract

An open problem about two new families of orthogonal polynomials was posed by Alhaidari. Here we will identify one of them as Wilson polynomials. The other family seems to be new but we show that they are discrete orthogonal polynomials on a bounded countable set with one accumulation point at 0 and we give some asymptotics as the degree tends to infinity.