Abstract
In this paper, by constructing contour integral and using Cauchy’s residue theorem, we provide a novel proof of Chu’s two partial fraction decompositions.
Highlights
The generalized harmonic numbers are defined by H0(r) = 0 and Hn(r) = n1 kr k=1 for n, r = 1, 2, . . . ; when r = 1, they reduce to the classical harmonic numbers Hn = Hn(1)
Proof The proof is similar to that of Theorem 1, and we only present the important steps and omit many details
A considerably large group of authors have made use of the so-called (p, q)-analysis by introducing a seemingly redundant parameter p in the already known results dealing with the classical q-analysis
Summary
1 Introduction The generalized harmonic numbers are defined by The complete Bell polynomials Bn(x1, x2, . Bruno formula and obtained several striking harmonic number identities from two partial fraction decompositions. We rewrite two main results of Chu. Theorem A ([4, Theorem 2]) Let λ, θ , and n be three natural numbers such that 0 ≤ θ < λ(n + 1).
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