UNIFORM ASYMPTOTIC EXPANSIONS FOR WHITI'AKER'S CONFLUENT HYPERGEOMETRIC FUNCTIONS*

The asymptotic behavior, as K-> o, of the Whittaker confluent hypergeometric functions MK. (z) and WK,, (z) is examined. Asymptotic expansions are derived in terms of Bessel and Airy functions, the results being uniformly valid for real values of K and such that 0-<//K _--< A< (A an arbitrary constant), and for all complex values of the argument z. Explicit error bounds are available for all the approximations.