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In this paper, by using the residue method of complex analysis, we obtain an explicit partial fraction decomposition for the general rational function x M (x + 1) n λ (M is any nonnegative integer, λ and n are any positive integers). As applications, we deduce the corresponding algebraic identities and combinatorial identities which are the corresponding extensions of Chu' results. We also give some explicit formulas of Apostol-type polynomials and harmonic Stirling numbers of the second kind. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]