=ADD=
=reftype=
14
=number=
02-21
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/2002/02-21.ps.gz
=year=
2002
=month=
11
=author=
Ahlgren; Scott + Paule; Peter + Schneider; Carsten
=title=
Computer Proofs of a New Family of Harmonic Number Identities
=abstract=
In this paper we consider five conjectured harmonic number identities
similar to those arising in the context of supercongruences for
Ap{\'e}ry numbers. The general object of this article is to discuss the
possibility of automating not only the proof  but also the discovery of
such formulas. As a specific application we consider two different
algorithmic methods to derive and to prove the five conjectured
identities. One is based on an extension of Karr's summation algorithm
in difference fields. The other method combines an old idea of Newton
(which has been extended by Andrews) with Zeilberger's algorithm for
definite hypergeometric sums.
=howpublished=
Submitted to Advances in Applied Mathematics
=sponsor=
SFB-grant F1305 of the Austrian FWF, NSF grant DMS 01-35477