Asymptotic and exact series representations for the incomplete Gamma functionP. 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 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.
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