=ADD=
=author=
Lisonek; Petr
=title=
The Performance of Gosper's Algorithm 	on Rational Function Inputs
=number=
91-31
=year=
1991
=sponsor=
 Austrian Ministery of Science and Research, Austrian Forschungsf"{o}rderungsfonds,
project no. P7220.
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1991/91-31.ps.gz
=abstract=
We prove a new observation concerning the behaviour of Gosper's algorithm: for
each proper rational function input, i.e.\ the degree of the numerator os less
than the degree of the denominator, Gosper's algorithm chooses the $k_0$-value
as the degree of the polynomial $f(n)$. Further we show that for proper
rational functions as inputs, the alternative degree bound for $f(n)$, namely
deg$p(n)$ - deg $q(n)$ + 1, also yields a solution but with less effort. This
results in a speed-up of Gosper's algorithm when it is running on proper
rational functions.
=location=
2
=owner=
2
=source=
3
=reftype=
14