Keywords:
$q$-Rice formula, $q$-identity, $q$-generalized harmonic number, Cauchy's integral formula, Faà di Bruno's formula
Abstract
In this paper, by means of the $q$-Rice formula we obtain a general $q$-identity which is a unified generalization of three kinds of identities. Some known results are special cases of ours. Meanwhile, some identities on $q$-generalized harmonic numbers are also derived.