The subject of the paper is the asymptotic stability analysis of the trivial equilibrium of a scalar and linear delay differential equation with one discrete delay and one (infinite) distributed delay. The kernel of the distributed term is of g-distribution type, and in particular, we make the specific choice  The goal of the article is to determine conditions on the parameters of the equation guaranteeing discrete delay-independent stability and, when such conditions are violated, showing which choices lead to destabilisation. The results are based on the exact analysis of the characteristic equation of the delay differential equation.

delay differential equation, distributed delay, characteristic equation, stability.