  The Sommerfeld and Brillouin forerunners generated in a single-resonance
absorbing medium by an incident step-modulated pulse are theoretically
considered in the double limit where the susceptibility of the medium is weak
and the resonance is narrow. Combining direct Laplace-Fourier integration and
calculations by the saddle-point method, we establish an explicit analytical
expression of the transmitted field valid at any time, even when the two
forerunners significantly overlap. We examine how their complete overlapping,
occurring for shorter propagation distances, originates the formation of the
unique transient currently named resonant precursor or dynamical beat. We
obtain an expression of this transient identical to that usually derived within
the slowly varying envelope in spite of the initial discontinuity of the
incident field envelope. The dynamical beats and 0Pi pulses generated by
ultra-short incident pulses are also briefly examined
