Error analysis in a uniform asymptotic expansion for the generalised exponential integral

DOI10.1016/S0377-0427(97)00026-5zbMath0870.33002OpenAlexW2141605681MaRDI QIDQ1360162

T. M. Dunster

Publication date: 8 September 1997

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(97)00026-5

zbMATH Keywords

error functionturning point theoryuniform asymptotic expansionsincomplete gamma functionsgeneralised exponential integral

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Approximation in the complex plane (30E10) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Asymptotic expansions of solutions to ordinary differential equations (34E05) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

Related Items (4)

Simplified Asymptotic Solutions of Differential Equations Having Two Turning Points, with an Application to Legendre Functions ⋮ Uniform convergence and computation of the generalized exponential integrals ⋮ Evaluation of generalized exponential integrals using multinomial expansion theorems ⋮ Error bounds for the uniform asymptotic expansion of the incomplete gamma function

Cites Work

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• Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters
• On the Lambert \(w\) function
• Error bounds for exponentially improved asymptotic solutions of ordinary differential equations having irregular singularities of rank one
• 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
• Uniform, Exponentially improved, Asymptotic Expansions for the Generalized Exponential Integral
• The Asymptotic Expansion of the Incomplete Gamma Functions
• Exponentially improved asymptotic solutions of ordinary differential equations. II. Irregular singularities of rank one
• Uniform asymptotic smoothing of Stokes’s discontinuities

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