Review of8 Computational Techniques for the Summation of Series Author: Anthony Sofo Kluwer Academic Publishers, New York, 2003 206 pages, $105.00 Review by Vladik Kreinovich, vladik@utep.edu Anyone who browsed through D. Knuth s Art of Computer Programming books knows that in many cases, the computational complexity of an algorithm be it worst-case or average-case complexity can be described in terms of recurrence relations or series. If we simply describe this complexity as, say, a sum of the series, we do not gain much: computing this sum is often not much faster than simply running the original algorithm, and analyzing how this complexity grows with the size of a problem is very di cult. If we can have an analytical expression for the corresponding sum, then the situation changes drastically: we can compute its value fast, and we can e ciently analyze its asymptotic properties. In his analysis of algorithms, Knuth encountered a few series for which the analytical expressions for the sum were already known, a lot of series for which he himself succeeded in deriving the corresponding analytical expressions (and quite a few cases in which he did not succeed). Many of his new cases
/lp/association-for-computing-machinery/review-of-computational-techniques-for-the-summation-of-series-by-76BEiTjD6c