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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