Asymptotic solutions of second-order linear differential equations having almost coalescent turning points, with an application to the incomplete gamma function

DOI10.1098/rspa.1996.0068zbMath0877.34011OpenAlexW2115698320MaRDI QIDQ3127887

T. M. Dunster

Publication date: 13 April 1997

Published in: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.1996.0068

zbMATH Keywords

incomplete gamma functionasymptotic approximationsparabolic cylinder functionssecond-order linear differential equation

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Linear ordinary differential equations and systems (34A30) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

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Simplified Asymptotic Solutions of Differential Equations Having Two Turning Points, with an Application to Legendre Functions ⋮ Error analysis in a uniform asymptotic expansion for the generalised exponential integral ⋮ Connection Problem of the First Painlevé Transcendent Between Poles and Negative Infinity ⋮ Application of uniform asymptotics to the connection formulas of the fifth Painlevé equation ⋮ Asymptotics of the eigenvalues of the rotating harmonic oscillator ⋮ On the connection problem for nonlinear differential equation

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