On the asymptotic behavior of the maximum absolute value of generalized Gegenbauer polynomials

TL;DR

This paper derives asymptotic estimates for the maximum absolute value of generalized Gegenbauer polynomials using properties of Jacobi polynomials, providing insights into their long-term behavior.

Contribution

It introduces new asymptotic estimates for generalized Gegenbauer polynomials based on classical Jacobi polynomial properties.

Findings

Asymptotic estimates for maximum absolute values derived

Enhanced understanding of polynomial behavior at large degrees

Connections established between Gegenbauer and Jacobi polynomials

Abstract

Using well-known facts on Jacobi polynomials, we derive some asymptotic estimates for the maximum absolute value of generalized Gegenbauer polynomials.