Incomplete gamma functions for large values of their variables

DOI10.1016/j.aam.2004.08.001zbMath1076.33001OpenAlexW1968678696MaRDI QIDQ2568106

Ester Pérez Sinusía, Chelo Ferreira, José Luis López

Publication date: 7 October 2005

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

Full work available at URL: https://doi.org/10.1016/j.aam.2004.08.001

zbMATH Keywords

asymptotic expansionsincomplete gamma functions

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Numerical approximation and evaluation of special functions (33F05) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

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Goodness of fit tests in terms of local levels with special emphasis on higher criticism tests ⋮ An efficient series approximation for the Lévy \(\alpha\)-stable symmetric distribution ⋮ The Gauss hypergeometric function \(F(a,b;c;z)\) for large \(c\) ⋮ Asymptotic expansions for the incomplete gamma function in the transition regions ⋮ Weighted integral and integro-differential inequalities ⋮ A monotonicity property of the composition of regularized and inverted-regularized gamma functions with applications ⋮ Performance criteria and discrimination of extreme undersmoothing in nonparametric regression ⋮ A simplification of Laplace's method: applications to the gamma function and Gauss hypergeometric function

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
• Asymptotische Eigenschaften der unvollständigen Gammafunktionen
• Uniform, Exponentially Improved, Asymptotic Expansions for the Confluent Hypergeometric Function and Other Integral Transforms
• The Asymptotic Expansion of the Incomplete Gamma Functions
• Uniform Approximations of Bernoulli and Euler Polynomials in Terms of Hyperbolic Functions
• Convergent asymptotic expansions of Charlier, Laguerre and Jacobi polynomials
• Exponential integral integral infinity 1 e-xtt -ndt for large values of n
• The Askey scheme for hypergeometric orthogonal polynomials viewed from asymptotic analysis

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