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.
Highlights
Three kinds of identities will be introduced 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
Mansour et al [15] established a q-analog for the rational sum identity (1.4): n
Summary
Three kinds of identities will be introduced in this paper. In the paper [21], Van Hamme gave the following identity n (−1)k−1 n q ( ) k+1 2 n. Guo and Zhang [12] made use of the Lagrange interpolation formula to give a generalization of Prodinger’s identity (1.3). They gave a generalization of Dilcher’s identity (1.2). Prodinger [18] made use of partial fraction decomposition and inverse pairs to present a more general formula:. Mansour et al [15] established a q-analog for the rational sum identity (1.4):. They gave a very nice bijective proof for the case λ = 1. In the recent paper [19], Prodinger established an interesting identity involving harmonic numbers:
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