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/i2005100666
 arXiv:
 arXiv:mathph/0501019
 Bibcode:
 2005EL.....71....1A
 Keywords:

 Mathematical Physics;
 Mathematics  Mathematical Physics
 EPrint:
 8 pages, 4 figures