Terminating asymptotic series of some integral transforms containing exponential type functions
We perform an asymptotic evaluation of integral transforms containing exponential type functions. Two cases are considered where the exponential type function is entire or meromorphic. For the integral with an entire exponential type function, it is shown that this produces a Poincaré expansion where the behavior is terminating. For the integral with meromorphic exponential type function, it also produces the Poincaré expansion that is terminating, but with the addition of the exponentially small terms which the Poincaré expansion misses out.