A q-analogue of Graf's addition formula for the Hahn-Exton q-Bessel   function
  An 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. 
Erik Koelink, Ren\'e F. Swarttouw