Laser pulses facilitate multiphoton contributions to the trident pair production , where the label L indicates a laser field dressed electron (e−) or positron (e+ ). We isolate the impact of the pulse envelope in the trident S matrix element, formulated within the Furry picture, in leading order of a series expansion in the classical nonlinearity parameter a0. Generally, the Fourier transform of the envelope carries the information on the pulse length, which becomes an easily tractable function in the case of a pulse envelope. The transition to a monochromatic laser wave can be handled in a transparent manner, as also the onset of bandwidth effects for short pulses can be factorized out and studied separately.