A uniform asymptotic expansion for the incomplete gamma function
type: Item
instance of: scholarly article
title: A uniform asymptotic expansion for the incomplete gamma function
zbMATH Open document ID: 1013.33002
DOI: 10.1016/S0377-0427(02)00553-8
published in: Journal of Computational and Applied Mathematics
publication date: 2003-02-23T00:00:00Z
review text: A new uniform asymptotic expansion is given for the incomplete gamma function \(\Gamma(a,z)\) valid for large \(z\). The expansion is compared with one developed by the reviewer [SIAM J. Math. Anal. 10, 757-766 (1979; Zbl 0412.33001)]. The coefficients of the new expansion are simpler to evaluate near the transition point \(a=z\), the domain of validity for the complex parameters \(a\) and \(z\) is smaller. In the new expansion the error function again gives the main approximation, higher terms are related with the error function (and with parabolic cylinder functions). Numerical examples are given to illustrate the accuracy of the expansion.
Mathematics Subject Classification ID: 33B20
zbMATH DE Number: 1872888
zbMATH Keywords: incomplete gamma function
zbMATH Keywords: uniform asymptotic expansion
author: Richard B. Paris
reviewed by: Nico M. Temme
MaRDI profile type: Publication
Wikidata QID: Q56271102
cites work: Q3218192
cites work: Computation of the incomplete gamma function ratios and their inverse
cites work: Q4765553
cites work: The asymptotic evaluation of certain integrals
cites work: Exponential integral integral infinity 1 e-xtt -ndt for large values of n
cites work: Q3671491
cites work: Asymptotics for the Kummer function of Bose plasmas
cites work: Q4764054
cites work: New asymptotic formulas for the Riemann zeta function on the critical line
cites work: An asymptotic representation for \(\zeta(\frac{1}{2}+it)\)
cites work: Q3312505
cites work: The Asymptotic Expansion of the Incomplete Gamma Functions
cites work: Q4764057
cites work: Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters
cites work: Asymptotische Eigenschaften der unvollständigen Gammafunktionen
cites work: Q3844537
cites work: On uniform asymptotic expansion of definite integrals
description: scientific article; zbMATH DE number 1872888