Uniform Asymptotics for the Incomplete Gamma
نویسنده
چکیده
We consider the asymptotic behavior of the incomplete gamma functions (?a; ?z) and ?(?a; ?z) as a ! 1. Uniform expansions are needed to describe the transition area z a, in which case error functions are used as main approximants. We use integral representations of the incomplete gamma functions and derive a uniform expansion by applying techniques used for the existing uniform expansions for (a; z) and ?(a; z). The result is compared with Olver's uniform expansion for the generalized exponential integral. A numerical veriication of the expansion is given in a nal section.
منابع مشابه
Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters
REPORTRAPPORT Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters Abstract We consider the asymptotic behavior of the incomplete gamma functions (?a; ?z) and ?(?a; ?z) as a ! 1. Uniform expansions are needed to describe the transition area z a, in which case error functions are used as main approximants. We use integral representations of the i...
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