A sequence that satisfies a relation
where are constants. The relation permits one to compute the terms of the sequence one by one, in succession, if the first terms are known. A classical example of such a sequence is the Fibonacci sequence (, ). A recursive series is a power series whose coefficients form a recursive sequence. Such a series represents an everywhere-defined rational function.
A good reference treating many aspects of such sequences is [a1].
|[a1]||A.J. van der Poorten, "Some facts that should be better known, especially about rational functions" R.A. Molin (ed.) , Number theory and applications (Proc. First Conf. Canadian Number Theory Assoc., Banff, April 1988) , Kluwer (1989) pp. 497–528|
Recursive sequence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Recursive_sequence&oldid=12807