This is particularly useful in finding closed form expressions for terms of linear recursive sequences, such as the Fibonacci numbers.

Nevertheless several analytical closed form expressions for the effect of such additional "perturbing forces" are still very useful.

Most stable distributions do not have a known closed form expression for their probability density functions.

The texture in each region is modeled by a multivariate normal distribution whose entropy has closed form expression.

A closed form expression for the series is not known, but it converges rapidly.

Largely based on the pentatonic scale, Chinese folk music is different from western traditional music, paying more attention to the form expression as well.

For higher values of N, there are no closed form expressions, but the solitons exist and they are all periodic with different periods.

For higher order solitons () we can use the following closed form expression:

A closed form expression for the so-called rabbit sequence:

Except for the special cases of and , no closed form expression for this probability distribution is known.