DELTA-FUNCTION EXPANSIONS, COMPLEX DELTA-FUNCTIONS AND THE STEEPEST DESCENT METHOD

Expansion of concentrated functions in terms of a delta function series is discussed with examples. The delta function is extended into the complex plane in the limit of the analytic Gaussian function. It is demonstrated that problems normally handled with the steepest descent method can be simply expressed as an integration of the delta function in the complex plane, which can be more easily grasped by students.