The asymptotic expansion of a generalised incomplete gamma function

We define a generalised incomplete gamma function 2(p)(a,z), which coincides with the familiar normalised function Q(a, z) = Gamma(a, z)/Gamma(a) when the integer parameter p = 1. It is shown that the large-z asymptotics of 2(p)(a,z) in the sector \argz\ < pip consists of p exponential expansions. In Re(z) > 0, all these expansions are recessive at infinity and form a sequence of increasingly subdominant exponential contributions. (C) 2003 Elsevier Science B.V. All rights reserved.