NAME: George E. Andrews

ADDRESS: 410 McAllister Building
Mathematics Dept.
Penn State University
University Park, PA 16802

EMAIL: andrews@math.psu.edu

Talk Title:  Search Algorithms in the Study of q-Series


Abstract:  We begin the talk with an account of some of the
algorithms that have been used in the study of partitions
and q-series.  We begin with the Euler-Ostmann algorithm.
Following this history we shall describe recent work (with
Arnold Knopfmacher, the late John Knopfmacher and Peter
Paule) on the generalized Engel algorithm.  Engel developed
an expansion for real numbers which provided a means of
testing for irrationality.  The Knopfmachers extended this
method to the theory of analytic functions.  We shall
show how it can be used to "discover," as well as prove,
results like the Rogers-Ramanujan identities.  We close
with some discussion of possible extensions of this
algorithm.
 
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