Rigorous state-to-state quantum calculations of the dynamics of the radiative association reaction He + H-2(+) --> HeH2+ + hnu are performed. For this purpose the appropriate methodology is described in detail and computational aspects facilitating the actual calculations of the resonances and the free-bound phototransition amplitudes are discussed. Under the assumptions that the reaction is a single-state process proceeding entirely on the ground electronic state potential energy surface of HeH2+ and that higher dissociation channels of the ion complex can be neglected, all resonances contributing to the association are determined and the rate constant as a function of temperature is calculated for the low-temperature interval 2 less than or equal to T less than or equal to 100 K. Its maximum value is predicted to be small, 2.1 X 10(-20) cm(3) s(-1) at a temperature of about 20 K. (C) 2003 American Institute of Physics.