Improvement of the degree setting in Gosper's algorithm
type: Item
instance of: scholarly article
title: Improvement of the degree setting in Gosper's algorithm
zbMATH Open document ID: 0872.33001
author: Petr Lisoněk
author: Peter Paule
author: Volker Strehl
published in: Journal of Symbolic Computation
publication date: 1996-02-20T00:00:00Z
review text: This paper provides a useful detailed analysis of Gosper's algorithm for indefinite hypergeometric summation; it will prove invaluable for readers wishing to understand and improve upon the algorithms employed to that end by familiar computing packages. The issue is, given polynomials \(\sigma\) and \(\tau\), to determine the sums \(\sum_{k=1}^n a_k\) for sequences \((a_k)\) given by recurrence relations \(a_k= (\sigma(k)/\tau(k)) a_{k-1}\). One of the crucial steps in Gosper's algorithm is the determination of a degree bound for a possible polynomial solution of the key difference equation associated to the summation. The present analysis of that problem deals with that matter and, to do that, gives an instructive introduction to the principles underlying the algorithm. No doubt, readers other than the reviewer will be amused by the eccentric behaviour of Apery's sequence in the present context.
Mathematics Subject Classification ID: 33-01
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 502898
zbMATH Keywords: hypergeometric series
zbMATH Keywords: summation algorithms
zbMATH Keywords: computational complexity
zbMATH Keywords: Gosper's algorithm
MaRDI profile type: Publication
OpenAlex ID: W2131914309
DOI: 10.1006/JSCO.1993.1043
description: scientific article; zbMATH DE number 502898