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Asymptotic and exact series representations for the incomplete Gamma function

Paolo Amore
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Abstract

Using a variational approach, two new series representations for the incomplete Gamma function are derived: the first is an asymptotic series, which contains and improves over the standard asymptotic expansion; the second is a uniformly convergent series, completely analytical, which can be used to obtain arbitrarily accurate estimates of $Γ(a,x)$ for any value of $a$ or $x$. Applications of these formulas are discussed.

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Paolo Amore. 2005-01-10. Asymptotic and exact series representations for the incomplete Gamma function. https://doi.org/10.1209/epl%2Fi2005-10066-6

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