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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.
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Regular Points of Differential Equations of the Second Order (Classic Reprint)
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Paperback. Zustand: New. Print on Demand. This book explores the mathematical solutions to second-order differential equations, focusing on techniques to find solutions expressed as power series. The author first considers the simplest case of differential equations with constant coefficients before moving on to more complex equations with variable coefficients. The book provides a way to determine the behavior of solutions near singular points and at infinity. These equations are essential in various scientific fields, including physics and engineering, and the author's research offers new insights into their analysis. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781528201834_0
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Regular Points of Differential Equations of the Second Order (Classic Reprint)
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