Bounds for an Integral Involving Whittaker Functions of the Second Kind

This note deals with the brief investigation of an integral involving Whittaker functions of the second kind, which is related to some Sturm-Liouville problems and is of interest in quickest change-point detection. We deduce some complete monotonicity results for Whittaker functions of the second kind and we derive (sharp) lower and upper bounds for different sets of the parameters for the integral in question.