Page:Philosophical Transactions - Volume 145.djvu/187

This page has been proofread, but needs to be validated.
mr. w.h.l. russell on the theory of definite integrals.

equations in finite terms would be practicable in very few cases. The following method of determining a well-known definite integral is here added, to show the connexion between previous investigations relative to definite integrals, and those given in the present memoir.

We know that
Hence remembering that
we find

I shall now enter on some investigations connected with Lagrange's theorem.

Let be an algebraical equation. Then Lagrange's theorem gives us the following series:—

If we apply the usual test of convergency to this series, we find that must be less than unity.

Then we see that

wherefore, since
we have

Hence we have