| Issue |
Europhys. Lett.
Volume 71, Number 1, July 2005
|
|
|---|---|---|
| Page(s) | 1 - 7 | |
| Section | General | |
| DOI | https://doi.org/10.1209/epl/i2005-10066-6 | |
| Published online | 27 May 2005 | |
Asymptotic and exact series representations for the incomplete Gamma function
Facultad de Ciencias, Universidad de Colima Bernal Díaz del Castillo 340, Colima, Colima, Mexico
Received:
16
February
2005
Accepted:
9
May
2005
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 
for any value of
a or x. Applications of these formulas are discussed.
PACS: 02.30.Mv – Approximations and expansions / 11.15.Bt – General properties of perturbation theory / 11.15.Tk – Other nonperturbative techniques
© EDP Sciences, 2005
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