ABSTRACT
The results of analyses of algorithms are rarely given by closed-form expressions. All the functions we look to approximate asymptotically are performance measures, or combinatorial counts; in other words, the functions are considered to be positive. A typical way to describe an asymptotic estimate (or approximation) is as a characterization of the behavior of the function as its argument grows, or that it captures the main dependence of the function on a large argument. Many problems in algorithmic analysis lead to sums for which we know no closed form. The problem of developing asymptotic estimates for such sums has been given much attention. Direct numerical evaluation of sums with alternating coefficients may be challenging because of subtraction operation involving large numbers that may result in losing significance.
