A common method in this form of modelling is to use recurrence relations.

These two cases include all possibilities, so the recurrence relation follows.

We can rearrange this to get a recurrence relation for A.

These values are easy to generate using the recurrence relation in the previous section.

A simple form of functional equation is a recurrence relation.

Every recurrence relation can be formulated as a difference equation.

This is a recurrence relation giving in terms of .

In fact, this is no longer a recurrence relation but a functional equation.

Find a closed formula for a sequence given in a recurrence relation.

The function can also be written as a recurrence relation:

In aid of this, we have the following recurrence relation:

However, "difference equation" is frequently used to refer to any recurrence relation.

This recurrence relation may be derived from that for the Bernoulli numbers.

The existence of these recurrence relations shows that for any base there are infinitely many self numbers.

Recurrence relations for the distribution of the test statistic in finite samples are available.

The following recurrence relation generates some base 10 self numbers:

Recurrence relations are equations to define one or more sequences recursively.

An example of a recurrence relation is the logistic map:

These recurrence relations are useful for discrete diffusion problems.

The most likely state sequence that produces the observations is given by the recurrence relations:

This latter form is the mathematical definition of factorial as a recurrence relation.

This explains the term of the recurrence relation.

An alternative approach is to set up a recurrence relation for the T(n) factor, the time needed to sort a list of size .

A more formal definition uses a recurrence relation.

In general it applies to any class of functions that can be defined by a three-term recurrence relation.