Asymptotic and exact series representations for the incomplete Gamma function

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

8 pages, 4 figures

References in corpus (2)

• Quantum Dynamics of the Slow Rollover Transition in the Linear Delta Expansion
• A method for classical and quantum mechanics

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