Asymptotic Limit of Continuous Dual Hahn Polynomial

TL;DR

This paper derives the asymptotic limit of the Continuous Dual Hahn Polynomial using the Darboux method, involving the construction and expansion of a comparison function related to its generating function.

Contribution

It introduces a novel application of the Darboux method to find the asymptotic behavior of Continuous Dual Hahn Polynomials.

Findings

Asymptotic limit derived for Continuous Dual Hahn Polynomial

Method involves constructing a comparison function from the generating function

Provides a simplified approach to asymptotic analysis

Abstract

Using Darboux method, we obtain an asymptotic limit for Continuous Dual Hahn Polynomial.The basic concept is to construct a comparison function which is the singular part of the generating function; then expand the comparison function. With little simplification and modification,the asymptotic limit is achieved.