On the use of Hadamard expansions in hyperasymptotic evaluation. II Complex variables

This paper extends the method of hyperasymptotic evaluation using absolutely convergent Hadamard expansions, developed in the first part, to the confluent hypergeometric functions of complex argument z. It is shown that the representation of this class of functions involves an infinite number of Hadamard expansions associated with a decreasing sequence of subdominant exponential levels for large \z \. Numerical examples involving the Bessel functions are given to illustrate the attainable levels of accuracy.