In mathematics, a recurrence relation is an equation that recursively defines a sequence, once one or more initial terms are given: each further term of the sequence is defined as a function of the preceding terms. The term difference equation sometimes (and for the purposes of this article) refers to a specific type of recurrence relation. However, "difference equation" is frequently used to refer to any recurrence relation. An example of a recurrence relation is the logistic map:
with a given constant r; given the initial term x0 each subsequent term is determined by this relation. Some simply defined recurrence relations can have very complex (chaotic) behaviours, and they are a part of the field of mathematics known as nonlinear analysis. Solving a recurrence relation means obtaining a closed-form solution: a non-recursive function of n.Watch the video below for further infromation on Recurrence relations.