On a General $q$-Identity

Aimin Xu


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.


$q$-Rice formula; $q$-identity; $q$-generalized harmonic number; Cauchy's integral formula; Faà di Bruno's formula

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