Some possible $q$-generalizations of harmonic numbers
  We study three different $q$-analogues of the harmonic numbers. As applications, we present some generating functions involving number theoretical functions and give the $q$-generalization of Gosper's exponential generating function of harmonic numbers. We involve also the $q$-gamma and $q$-digamma function. 
Istv\'an Mez\H{o}
math.CO