Symbolic Summation: Algorithms and Missed Opportunities
Peter Paule, RISC, Johannes Kepler University, Austria
Friday, September 13, 2002, at U. of Waterloo.
Abstract:
The problem of simplifying complicated sum expressions arises not
only in special functions but in many mathematical fields.
Nevertheless, symbolic algorithms that assist in this task do not have
a very long history.
The starting point of symbolic summation with the computer is
Gosper's algorithm (1978), a decision procedure for indefinite
hypergeometric summation. Despite being a first breakthrough, for a
long time its applicability has been considered as quite restricted
since most hypergeometric summations arising in practice are definite
ones. Zeilberger's 'creative telescoping' (1990) dissolved this
limitation. Since then symbolic summation has turned into an active
subarea of computer algebra on its own.
This talk presents a survey on algorithms and methods for
definite (multiple) sums along a historical chain of missed
opportunities.
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