Page:Philosophical Transactions - Volume 145.djvu/187

168 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.

I shall now enter on some investigations connected with theorem.

Let $$1-y+\alpha y^r=0$$ be an algebraical equation. Then theorem gives us the following series:&mdash;

If we apply the usual test of convergency to this series, we find that $$(r- 1)\alpha$$ must be less than unity.

Then we see that