  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 low-order delay-differential equations of retarded type, 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 of arbitrary order
including a single delay in the system's representation. More precisely, an
interesting link between characteristic functions with a real root of maximal
multiplicity and Kummer's confluent hypergeometric functions is exploited. We
also provide examples illustrating our main result.
