Excerpt from Regular Points of Differential Equations of the Second Order We shall find it convenient to postpone the proof of this extremely important theorem until later, and to go on at once to the following, Definition A regular point of the equation (1) is a point at which p does not become infinite to an order higher than the first or q to an order higher than the second. It will be seen that all ordinary points and some singular points are included among the regular points. The other singular points at which p becomes infinite to an order higher than the first or q to an order higher than the second or at which both of these things happen we shall naturally speak of as irregular points. In the following sections we shall obtain in the neighborhood of regular points solutions of (1) in the form of series and in the course of this work we shall obtain as a special case the fundamental theorem above given concern ing non-singular points. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.