Identities involving rational sums by inversion and partial fraction decomposition

Some More Identities Involving Rational Sums

The representation of sums in closed form can in some cases be achieved through a variety of different methods, including transform techniques, W–Z methods, Riordan arrays and integral representations. The interested reader is referred to the works of Egorychev [2], Gould [3], Merlini, Sprugnoli and Verri [4], Petkovšek, Wilf and Zeilberger [5] and Sofo [6], [7] and [8]. Recently Diaz-Barrero e...

Partial Fraction Decompositions and Trigonometric Sum Identities

The partial fraction decomposition method is explored to establish several interesting trigonometric function identities, which may have applications to the evaluation of classical multiple hypergeometric series, trigonometric approximation and interpolation. 1. Outline and introduction Recently, in an attempt to prove, through the Cauchy residue method, Dougall’s theorem (Dougall [6, 1907], se...

Partial-Fraction Decomposition Approach to the M/H2/2 Queue

Here, a two server queueing system with Poisson arrivals and two different types of customers (M/H2/2 queue) is analyzed. A novel straightforward method is presented to acquire the exact and explicit forms of the performance measures. First, the steady state equations along with their Z-transforms are derived for the aforementioned queueing system. Using some limiting behaviors of the steady-st...

Inequalities and Identities Involving Sums of Integer Functions

The floor and ceiling functions map a real number to the largest previous or the smallest following integer, respectively. More precisely, the floor function ⌊x⌋ is the largest integer not greater than x and the ceiling function ⌈x⌉ is the smallest integer not less than x. Iverson [7, p. 127] introduced this notation and the terms floor and ceiling in the early 1960’s and now this notation is s...

Binomial Sums and Identities