2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169040In this paper we study the positivity of the generalized $q$-translation associated with the $q$-Bessel Hahn Exton function which is deduced by a new formulation of the Graf's addition formula related to this function.Classical Analysis and ODEs33D15 (Primary); 33D60 (Secondary)On the Graf's addition theorem for Hahn Exton q-Bessel functiontext