Definition:Recursive Sequence/Recurrence Relation
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Definition
The equation which defines a recursive sequence is called a recurrence relation or difference equation.
Examples
Fibonacci Sequence
The classic example of a recursive sequence is the Fibonacci sequence:
- $F_n = F_{n - 1} + F_{n - 2}$
such that $F_1 = F_2 = 1$.
Also known as
A recurrence relation is also known as a recursive relation.
A recurrence relation can also be seen referred to as a difference equation, and vice versa.
However, a difference equation is in fact a particular type of recurrence relation, and the two are not strictly synonymous.
Also see
- Results about recurrence relations can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): recurrence relation
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): recurrence relation