Uniform asymptotic expansions for Gegenbauer polynomials and related functions via differential equations having a simple pole

DOI10.1007/s00365-023-09645-1arXiv2209.10716MaRDI QIDQ6126174

T. M. Dunster

Publication date: 9 April 2024

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.10716

zbMATH Keywords

Chebyshev polynomialsasymptotic expansionsGegenbauer polynomialsultraspherical polynomialsWKB methodssimple poles

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Asymptotic expansions of solutions to ordinary differential equations (34E05) Asymptotics and summation methods for ordinary differential equations in the complex domain (34M30)

Related Items (1)

Coulomb Green’s function and an addition formula for the Whittaker functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic approximations for the Jacobi and ultraspherical polynomials, and related functions
• Computation of asymptotic expansions of turning point problems via Cauchy's integral formula: Bessel functions
• A uniform asymptotic expansion for Jacobi polynomials via uniform treatment of Darboux's method
• Uniform asymptotic expansion of the Jacobi polynomials in a complex domain
• Convergent Expansions for Solutions of Linear Ordinary Differential Equations Having a Simple Pole, with an Application to Associated Legendre Functions
• A Uniform Asymptotic Expansion of the Jacobi Polynomials with Error Bounds
• ESTIMATES FOR THE ERROR TERM IN A UNIFORM ASYMPTOTIC EXPANSION OF THE JACOBI POLYNOMIALS
• Liouville-Green expansions of exponential form, with an application to modified Bessel functions
• Simplified error bounds for turning point expansions
• Nield--Kuznetsov Functions and Laplace Transforms of Parabolic Cylinder Functions
• Integrals with nearly coincident branch points: Gegenbauer polynomials of large degree
• Uniform Asymptotic Expansions of the Jacobi Polynomials and an Associated Function

This page was built for publication: Uniform asymptotic expansions for Gegenbauer polynomials and related functions via differential equations having a simple pole