Asymptotic and exact series representations for the incomplete Gamma function

Details Asymptotic and exact series representations for the incomplete Gamma function Asymptotic and exact series representations for the incomplete Gamma function

2005-01-10

arxiv.org/abs/math-ph/0501019v1

Europhysics Letters 71, 1-7 (2005)

Physics

Mathematical Physics

8 pages, 4 figures

Scientific paper

10.1209/epl/i2005-10066-6

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 $\Gamma(a,x)$ for any value of $a$ or $x$. Applications of these formulas are discussed.

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