  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.
