Recurrent Sequence

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Recurrent Sequence


a sequence a0, a1 a2, … that satisfies a relationship in the form

an + p + C1an + p - 1 + … + Cpan = 0

where C1, … ,Cp are constants. This relationship makes it possible to calculate, one after another, the members of the sequence if the first p members are known. The Fibonacci sequence 1, 1, 2, 3, 5, 8, … (a0 = 1, a1 = 1, …, an + 2 = an + i + an) is a classical example of a recurrent sequence. The origin of the term “recurrent sequence” is associated with the name of A. de Moivre, who regarded power series a0 + a1x + a2x2 … with coefficients forming a recurrent sequence as being “recurrent series.” Such series always portray rational functions.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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