# Uniform, exponentially improved, asymptotic expansions for the generalized exponential integral

@article{Olver1991UniformEI,
title={Uniform, exponentially improved, asymptotic expansions for the generalized exponential integral},
author={Frank W. J. Olver},
journal={Siam Journal on Mathematical Analysis},
year={1991},
volume={22},
pages={1475-1489}
}
• F. Olver
• Published 1 September 1991
• Mathematics
• Siam Journal on Mathematical Analysis
By allowing the number of terms in an asymptotic expansion to depend on the asymptotic variable, it is possible to obtain an error term that is exponentially small as the asymptotic variable tends to its limit. This procedure is called “exponential improvement.” It is shown how to improve exponentially the well-known Poincare expansions for the generalized exponential integral (or incomplete Gamma function) of large argument. New uniform expansions are derived in terms of elementary functions…
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