Volume 71, Number 1, July 2005
|Page(s)||1 - 7|
|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
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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