A simplification of Laplace's method: applications to the gamma function and Gauss hypergeometric function

DOI10.1016/j.jat.2008.09.004zbMath1194.33004OpenAlexW2024035912MaRDI QIDQ1040870

Ester Pérez Sinusía, José Luis López, Pedro J. Pagola

Publication date: 26 November 2009

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2008.09.004

zbMATH Keywords

Stirling's formulaasymptotic expansion of integrals

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (10)

An explicit formula for the coefficients in Laplace's method ⋮ An explicit formula for the coefficients of the saddle point method ⋮ Uniform representations of the incomplete beta function in terms of elementary functions ⋮ Convergent expansions of the incomplete gamma functions in terms of elementary functions ⋮ On the asymptotic Laplace method and its application to random chaos ⋮ A Systematic “Saddle Point Near a Pole” Asymptotic Method with Application to the Gauss Hypergeometric Function ⋮ Error bounds and exponential improvements for the asymptotic expansions of the gamma function and its reciprocal ⋮ Asymptotics of the first Appell functionF₁with large parameters ⋮ A convergent and asymptotic Laplace method for integrals ⋮ Asymptotics of the first Appell functionF₁with large parameters II

Cites Work

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• Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters
• A uniform asymptotic expansion for the incomplete gamma function
• The Gauss hypergeometric function \(F(a,b;c;z)\) for large \(c\)
• Incomplete gamma functions for large values of their variables
• The Laplace's and steepest descents methods revisited
• Computing the Coefficients in Laplace's Method

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