Recursive sequence

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recurrent sequence

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
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Recursive sequence. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article