STOKES LINE-WIDTH

The concept of Stokes line width is introduced for the asymptotic expa nsions of functions near an essential singularity. Explicit expression s are found for functions (switching functions) that ''switch on'' the exponentially small terms for the Dawson integral, Airy function, and the gamma function. A different, more natural representation of a fun ction, not associated with expansion in an asymptotic series, in the f orm of dominant and recessive terms is obtained by a special division of the contour integral which represents the function into contributio ns of higher and lower saddle points. This division leads to a narrowe r, natural Stokes line width and a switching function of an argument t hat depends on the topology of the lines of steepest descent from the saddle point.