A uniform asymptotic expansion for the incomplete gamma function

We describe a new uniform asymptotic expansion for the incomplete gamma function Γ( a, z) valid for large values of z. This expansion contains a complementary error function of an argument measuring transition across the point z= a (which is different from that in the well-known uniform expansion fo...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 148; no. 2; pp. 323 - 339
Main Author Paris, R.B.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 15.11.2002
Elsevier
Subjects
Exact sciences and technology
Incomplete gamma functions
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Sciences and techniques of general use
Special functions
Uniform asymptotic expansions
Incomplete gamma functions
Uniform asymptotic expansions
Incomplete
Asymptotic approximation
Asymptotic expansion
Error estimation
Gamma function
Special function
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Summary:We describe a new uniform asymptotic expansion for the incomplete gamma function Γ( a, z) valid for large values of z. This expansion contains a complementary error function of an argument measuring transition across the point z= a (which is different from that in the well-known uniform expansion for large a of Temme), with easily computable coefficients that do not involve a removable singularity at z= a. Our expansion is, however, valid in a smaller domain of the parameters than that of Temme. Numerical examples are given to illustrate the accuracy of the expansion.
Bibliography:ObjectType-Article-2
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ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(02)00553-8