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Abstract: The
applicability
or terminating
condition
for the ordinary
case of Zeilberger's
algorithm
was recently
obtained
by Abramov.
For the q-
analogue,
the question
of whether
a bivariate
q-hypergeometric
term has
a qZ-pair
remains open.
Le has found
a solution
to this problem
when the
given bivariate
q-hypergeometric
term is a
rational
function
in certain
powers of
q. We solve
the problem
for the general
case by giving
a char- acterization
of bivariate
q-hypergeometric
terms for
which the
q-analogue
of Zeilberger's
algorithm
terminates.
Moreover,
we give an
algorithm
to determine
whether a
bivariate
q-hypergeometric
term has
a qZ-pair.
AMS Classification: 33F10, 68W30.
Keywords:
q-Zeilberger algorithm, q-hypergeometric term,
Z-pair, qZ-pair, proper hypergeometric term, q-proper
hypergeometric term.
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