### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Brian Nakamura**, Rutgers University, bnaka {at} math [dot] rutgers [dot] edu
** Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Where is the cheapest equation?

Speaker: **Manuel Kauers**, Research Institute for Symbolic Computation, J. Kepler University, Linz, Austria

Date: ** Monday, September 26, 2011, 5:00pm (Note special day!)
**

ROOM CHANGE: CoRE 431 (DIMACS Seminar Room)

Location: CoRE 431 (DIMACS Seminar Room), Busch Campus, Piscataway, NJ

Abstract:

Zeilberger's celebrated method of creative telescoping
computes equations for given definite sums or
integrals. These equations are linear recurrence or
differential equtions of a certain finite order r with
polynomial coefficients of some degree d. For designing
efficient summation software, it is useful to know in
advance for which pairs (r,d) there will exist a solution of
order r and degree d. These pairs (r,d) form a certain
region in N^2, whose precise shape was not well understood
until now. Together with Shaoshi Chen, we have recently
determined a curve which provides a surprisingly accurate
description of the boundary of this region. We will not make
an attempt at explaining our technical derivation of this
curve in the talk, but we will show how its knowledge can be
used to determine, for example, the pair (r,d) for which the
computational cost is minimal. Perhaps surprisingly, it
turns out that this is not the pair where r is minimal.

See: http://www.math.rutgers.edu/~bnaka/expmath/