Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters

@article{Temme1996UniformAF,
  title={Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters},
  author={N. Temme},
  journal={Methods and applications of analysis},
  year={1996},
  volume={3},
  pages={335-344}
}
  • N. Temme
  • Published 1996
  • Mathematics
  • Methods and applications of analysis
We consider the asymptotic behavior of the incomplete gamma functions $gamma (-a,-z)$ and $Gamma (-a,-z)$ as $atoinfty$. Uniform expansions are needed to describe the transition area $z sim a$, 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 $gamma (a,z)$ and $Gamma (a,z)$. The result is compared with Olver's uniform… Expand
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