An urn model associated with the Jacobi polynomials

TL;DR

This paper introduces an urn model that results in a random walk explicitly solvable using Jacobi polynomials, linking combinatorial models with special functions.

Contribution

The paper presents a novel urn model connected to Jacobi polynomials, providing explicit solutions for the associated random walk.

Findings

Explicit solution for the random walk using Jacobi polynomials

New connection between urn models and special functions

Potential applications in probabilistic modeling

Abstract

We consider an urn model leading to a random walk that can be solved explicitly in terms of the well known Jacobi polynomials.