Conical functions with one or both parameters large

DOI10.1017/S0308210500014864zbMath0736.33002MaRDI QIDQ3984125

T. M. Dunster

Publication date: 27 June 1992

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

uniform asymptotic expansionsassociated Legendre functionsconical functions

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items

Large parameter cases of the Gauss hypergeometric function ⋮ In-plane dynamics of membranes having constant curvature ⋮ Nodal domains of Maass forms. I ⋮ Fundamental solutions and Gegenbauer expansions of Helmholtz operators in Riemannian spaces of constant curvature ⋮ Computation of a numerically satisfactory pair of solutions of the differential equation for conical functions of non-negative integer orders ⋮ Approximating with the Liouville-Green ⋮ Quantitative quantum ergodicity and the nodal domains of Hecke-Maass cusp forms ⋮ Computing toroidal functions for wide ranges of the parameters ⋮ Evaluation of the modified Bessel function of the third kind of imaginary orders

Cites Work

• Unnamed Item
• Uniform Asymptotic Solutions of Second-Order Linear Differential Equations Having a Double Pole with Complex Exponent and a Coalescing Turning Point
• Uniform Asymptotic Solutions of a Class of Second-Order Linear Differential Equations Having a Turning Point and a Regular Singularity, with an Application to Legendre Functions
• Legendre functions with both parameters large