Summation algorithms for Stirling number identities

We consider a class of sequences defined by triangular recurrence equations. This class contains Stirling numbers and Eulerian numbers of both kinds, and hypergeometric multiples of those. We give a sufficient criterion for sums over such sequences to obey a recurrence equation, and present algorithms for computing such recurrence equations efficiently. Our algorithms can be used for verifying many known summation identities about Stirling numbers instantly, and also for discovering new identities. Key words: Symbolic Summation, Stirling Numbers Find an efficient way to extend the Gosper-Zeilberger algorithm from hypergeometric terms to terms that may involve Stirling numbers. Graham, Knuth, Patashnik [4]

• Type: Journal
• Year: 2007
• Where: JSC
• Authors: Manuel Kauers
• Keywords: JSC 2007, Recurrence Equations, Stirling Numbers, Triangular Recurrence Equations