Abstract
In this paper, by using the residue method of complex analysis, we obtain a q-analogue for partial-fraction decomposition of the rational function xM(x+1)nλ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\frac{x^{M}}{(x+1)^{\\lambda}_{n}}$\\end{document}. As applications, we deduce the corresponding q-algebraic and q-combinatorial identities which are the q-extensions of Chu’ results.
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