An important question of ongoing interest for linear time-delay systems is to provide conditions on its parameters guaranteeing exponential stability of solutions. Recent works have explored spectral techniques to show that, for some delay-differential equations of retarded type of low order, spectral values of maximal multiplicity are dominant, and hence determine the asymptotic behavior of the system, a property known as multiplicity-induced-dominancy. This work further explores such a property and shows its validity for general linear delay-differential equations of retarded type and arbitrary order with a single delay, exploiting for that purpose an interesting link between characteristic functions with a root of maximal multiplicity and Kummer's confluent hypergeometric functions.