[en] In some problems of the mathematical theory of particle counters, film or filmless measurements of track ionization in high energy physics, queueing theory, random walks, etc., the classes of semirecurrent and m-semirecurrent events appear. In the paper the numerical estimates of the probabilistic formulae corresponding to the probability of the first occurrence of an event at the nth trial are studied. Very precise and computationally convenient formulae, are presented. The application of the theory to the counters with prolonging dead time and an illustrative numerical example are given