A number of other equivalent expressions are available.

This gives yet another equivalent expression for Carol numbers, .

A normal form is an equivalent expression that cannot be reduced any further under the rules imposed by the form.

Within the context of a logical proof, logically equivalent expressions may replace each other.

Jerk is defined by any of the following equivalent expressions:

If he didn't say that or an equivalent expression, he wasn't your friend.

They always have an equivalent expression using a preposition + accusative.

One can use the quality factor to substitute with an equivalent expression:

An equivalent expression gives the correlation coefficient as the mean of the products of the standard scores.

Again, a rigorous proof is needed for the fact that does not admit an equivalent regular expression of lower star height.