closed form in a sentence

Examples

1. The closed form follows from the master theorem.
2. Most stable distributions do not have a known closed form expression for their probability density functions.
3. Nevertheless, closed form expressions for the transformation matrices will be given below using group theoretical arguments.
4. The determinant can be expressed in closed form, as a special case of the Cauchy determinant.
5. :I doubt there is a closed form expression.
6. Essentially, by using a Taylor expansion one derives a closed form relation between these two representations.
7. Of particular interest are solutions in closed form.
8. Prior to World War I, the cooperation of the general staffs of both countries assumed closer forms.
9. For higher order solitons ( N > 1 ) we can use the following closed form expression:
10. Many expressions which are relatively simple do not have integrals that can be expressed in closed form.