The Summation of Rational Functions by an Extended Gosper Algorithm

✍ Scribed by D.E.G. Malm; T.N. Subramaniam

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 414 KB
• Volume: 19
• Category: Article
• ISSN: 0747-7171
• DOI: 10.1006/jsco.1995.1018

✦ Synopsis

The rational functions form the most elementary class of functions for which the problem of summation or antidifferencing is not straightforward. Gosper's algorithm finds the antidifference of a rational function only if that antidifference is itself a rational function. We present an algorithm based upon Gosper's method which finds the rational part of the antidifference and the purely transcendental summand, i.e., a summand whose antidifference can be expressed entirely as a sum of digamma functions and derivatives of digamma functions. This algorithm is analogous to Horowitz's improvement of the Hermite-Ostrogradski method for finding the antiderivative of a rational function. An earlier algorithm of Moenck is the analogue of the Hermite-Ostrogradski method itself. Our algorithm requires less work than Moenck's.