Simplified Asymptotic Solutions of Differential Equations Having Two Turning Points, with an Application to Legendre Functions

DOI10.1111/j.1467-9590.2011.00519.xzbMath1254.34018OpenAlexW1823342050MaRDI QIDQ2890956

T. M. Dunster

Publication date: 12 June 2012

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/j.1467-9590.2011.00519.x

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Spherical harmonics (33C55)

Related Items (2)

Asymptotics of prolate spheroidal wave functions ⋮ ASYMPTOTIC AND CONVERGENT EXPANSIONS FOR SOLUTIONS OF THIRD-ORDER LINEAR DIFFERENTIAL EQUATIONS WITH A LARGE PARAMETER

Uses Software

• DLMF

Cites Work

• Asymptotics of the eigenvalues of the rotating harmonic oscillator
• Error analysis in a uniform asymptotic expansion for the generalised exponential integral
• Asymptotic solutions of second-order linear differential equations having almost coalescent turning points, with an application to the incomplete gamma function
• Asymptotics of the generalized exponential integral, and error bounds in the uniform asymptotic smoothing of its Stokes discontinuities
• Second-order linear differential equations with two turning points
• Legendre functions with both parameters large
• Second-Order Differential Equations with Fractional Transition Points
• ON THE CHOICE OF STANDARD SOLUTIONS FOR A HOMOGENEOUS LINEAR DIFFERENTIAL EQUATION OF THE SECOND ORDER

This page was built for publication: Simplified Asymptotic Solutions of Differential Equations Having Two Turning Points, with an Application to Legendre Functions