Series Solution of Linear Differential Equations

Extract

The object of this article is to draw attention to a point in connection with the above topic which, as far as the memories of the books I read and of those which I have more recently read vicariously or had summarised to me, seems to have been entirely overlooked. This is the existence of what I term the “index interval”, associated with, and clearly discernible in, the differential equation itself, the recognition and use of which both simplifies the presentation and removes the obscurity surrounding points in connection with the intrusion of logarithmic terms into the solution of some equations of this type.