ABSTRACT
Recently M. V. Berry has provided a new interpretation of Stokes’ phenomenon in which the change in form of a compound asymptotic expansion occurs smoothly, albeit very rapidly, as a Stokes line is crossed. Berry’s analysis is based on R. B. Dingle’s theory of terminants, and is therefore quite formal. In this paper new analysis is developed to place the theories of both Dingle and Berry on rigorous mathematical foundations. The analysis is illustrated by application to Macdonald’s modified Bessel function, the generalized exponential integral and one of the confluent hypergeometric functions, but the method, like the methods of Dingle and Berry, is quite general.
