Europhys. Lett.
Volume 71, Number 1, July 2005
Page(s) 1 - 7
Section General
Published online 27 May 2005
Europhys. Lett., 71 (1), pp. 1-7 (2005)
DOI: 10.1209/epl/i2005-10066-6

Asymptotic and exact series representations for the incomplete Gamma function

P. Amore

Facultad de Ciencias, Universidad de Colima Bernal Díaz del Castillo 340, Colima, Colima, Mexico

received 16 February 2005; accepted in final form 9 May 2005
published online 27 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 $\Gamma(a,x)$ for any value of a or x. Applications of these formulas are discussed.

02.30.Mv - Approximations and expansions.
11.15.Bt - General properties of perturbation theory.
11.15.Tk - Other nonperturbative techniques.

© EDP Sciences 2005