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 Γ(a,x) for any value of a or x. Applications of these formulas are discussed.
- Publication:
-
EPL (Europhysics Letters)
- Pub Date:
- July 2005
- DOI:
- 10.1209/epl/i2005-10066-6
- arXiv:
- arXiv:math-ph/0501019
- Bibcode:
- 2005EL.....71....1A
- Keywords:
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- Mathematical Physics;
- Mathematics - Mathematical Physics
- E-Print:
- 8 pages, 4 figures