Abstract
AbstractIn this paper, by using the residue method of complex analysis, we obtain an explicit partial fraction decomposition for the general rational function $\frac{x^{M}}{(x+1)^{\lambda}_{n}}$
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.
Funder
Natural Science Foundation Project of Chongqing, Chongqing Science and Technology Commission
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis