Abstract A certain interest in the experimental nuclear physic community has been expressed for the precise detection of the β-shape of low Q-value decays, such as ⁹Tc →⁹⁹ Ru+e ⁻+ v ¯ e , tied to the search for the absolute mass of the neutrino. The necessity of a reliable way to compute the single-particle matrix elements for second forbidden operators has driven the implementation of a general algorithm to obtain the nuclear matrix elements for any given transition of generic forbiddenness K. Particular attention is then placed on the accuracy of the approximations commonly used in this context.