Page:Philosophical Transactions - Volume 145.djvu/182

Rh The following are instances of the application of this method obtained by using series I., III., IV.:&mdash;

Again, we know that

from which we may deduce the following:

Now consider the series

where ($$\alpha$$) is greater than $$\beta$$. Then by the above formula

and we find for the sum of the series,

In like manner we can find the sum of the series

where $$\alpha$$ is greater than $$\beta$$, $$\alpha'$$ than $$\beta'$$.