Sentence examples for above identity from inspiring English sources

Substituting the above identity into (29), we have the following.

The following expression can be written from the above identity.

In that case, the above identity statement (H) would have been false.

By considering the above identity in (2.3), we can easily state the following theorem.

In this paper we give the following generalizations of the above identity.

We include the proof, though its similar to that of the above identity.

Thus, using the above identities, we can write.

We also consider the following identities: By the above identities and also by the equation.

If (t=infty), then the two last terms of the above identities are 1.

All the above identities play an important role in the study of Parisian ruin.

(2.11) Finally, we note that the above identities hold for (n=2,3,4).