2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152903An addition and product formula for the Hahn-Exton $q$-Bessel function, previously obtained by use of a quantum group theoretic interpretation, are proved analytically. A (formal) limit transition to the Graf addition formula and corresponding product formula for the Bessel function is given.Classical Analysis and ODEsQuantum Algebratext