DiDonato (1978) gives a simple approximation for the function (which is related to the incomplete gamma function by a change of variables) for real and large positive . This takes the form , approximately, where and is shown to produce an absolute error as .
Luke (1969b, p. 186) gives hypergeometric polynomial representations that converge uniformly on compact subsets of the -plane that exclude and are valid for .
Luke (1975, p. 103) gives Chebyshev-series expansions for and related functions for .
Luke (1975, p. 106) gives rational and Padé approximations, with remainders, for and for complex with .
Verbeeck (1970) gives polynomial and rational approximations for , approximately, where denotes a quotient of polynomials of equal degree in .