Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

Title: A Solution to Exercise 95

Speaker: **Manuel Kauers**, Research Institute for Symbolic Computation, Hagenberg, Austria

Date: Thursday, July 26, 2007 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

The 1994 edition of Concrete Mathematics (Graham/Knuth/Patashnik) includes a research problem asking for extending "the Gosper-Zeilberger algorithm from hypergeometric terms to terms that may involve Stirling numbers". In the talk, we propose a solution to this problem. That is, we will (a) define a class of sequences that includes Stirling numbers, Eulerian numbers and hypergeometric multiples of these, (b) give a sufficient criterion for sums over such sequences to obey a recurrence equation, and (c) present algorithms for computing such a recurrence equation efficiently.