Artículos relacionados a A Contribution to the Theory of Linear Homogeneous...
A Contribution to the Theory of Linear Homogeneous Geometric Difference Equations (Q-Difference Equations) (Classic Reprint) - Tapa blanda
Sinopsis
Excerpt from A Contribution to the Theory of Linear Homogeneous Geometric Difference Equations (Q-Difference Equations)
In order to give a survey of the subject treated in this paper, I will here indicate the contents -of its particular sections. In 1 the main properties Of geometric factorial series are summarized. In 5 2 the proof of the existence of a system of solutions of the difference equation in question is given. In 3 these solutions are examined with regard to their asymptotic character and a proof of their linear independence is given. In 4 an examination of the analytic character Of the solutions is undertaken, and the solutions given by Grevy and Carmichael are de duced. In 5 some applications to particular equations are made. The list of literature p. 43 contains only works quoted in the paper. Of these I will especially mention the already cited works of Frobenius and nor lund, of which I have made frequent'use.
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.
"Sinopsis" puede pertenecer a otra edición de este libro.
Reseña del editor
Excerpt from A Contribution to the Theory of Linear Homogeneous Geometric Difference Equations (Q-Difference Equations)
In order to give a survey of the subject treated in this paper, I will here indicate the contents -of its particular sections. In 1 the main properties Of geometric factorial series are summarized. In 5 2 the proof of the existence of a system of solutions of the difference equation in question is given. In 3 these solutions are examined with regard to their asymptotic character and a proof of their linear independence is given. In 4 an examination of the analytic character Of the solutions is undertaken, and the solutions given by Grevy and Carmichael are de duced. In 5 some applications to particular equations are made. The list of literature p. 43 contains only works quoted in the paper. Of these I will especially mention the already cited works of Frobenius and nor lund, of which I have made frequent'use.
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.
Reseña del editor
Excerpt from A Contribution to the Theory of Linear Homogeneous Geometric Difference Equations (Q-Difference Equations)
Introduction. A functional relation of the following type i= nA.(a:).u(a:q ) = 0, (1) 1 = 0 where Af(x), A(x),. -(0:)are known functions of the complex variable Xand where qis a real or imaginary constant while u(x) is the function to be determined, may be termed a linear homogeneous geometric difference equation (or 7-difference equation) of the n-th order. The aim of the present paper is to bring the theory of these equations, at least on some points, to the same degree of perfection as the theories of the corresponding differential equations and arithmetic (ordinary) difference equations as they have been built up the former principally by Fuchs and Frobenius (1)the latter by Norlund (1).This equation(1) is a particular case of a general class of functional relations considered by Grevy (1), following ideas set forth by Ka-nigs (1), (2), (3).The equation(1) has then been treated in detail by Carmichael(1), who employs the method of successive approximations. He also indicates a possibility of solving the equation by aid of power series, which idea has then been worked out in a particular case by Mason(1). In a still more particular case power series have been used already by Heine(1) and Thomae (1), (2)and later on by Jackson(4) and Smith(1), It is, however, possible to replace the power series by another class of series, which may be termed geometric factorial series. These series appear in many respects to be more natural to the problem in question, just as arithmetic (ordinary) Such a number placed in a parenthesis close by a name refers to the list of literature p.43.
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.
"Sobre este título" puede pertenecer a otra edición de este libro.
Resultados de la búsqueda para A Contribution to the Theory of Linear Homogeneous...
Imagen del vendedor
A Contribution to the Theory of Linear Homogeneous Geometric Difference
Impresión bajo demandaLibrería: Forgotten Books, London, Reino Unido
Calificación del vendedor: 5 de 5 estrellas
Paperback. Condición: New. Print on Demand. This book provides a foundational approach to understanding linear homogeneous geometric difference equations (q-difference equations) and their solutions. The theory behind these equations is developed in a manner analogous to the theories of differential equations and arithmetic difference equations. The author begins with a review of geometric factorial series, which are essential for the development of solutions to q-difference equations. The book proceeds to provide a systematic method for finding solutions to these equations, with the solutions expressed in terms of geometric factorial series. The author also investigates the analytic character of these solutions and provides a thorough examination of their asymptotic behavior. The significance of this book lies in its contribution to the theory of linear homogeneous geometric difference equations, providing a comprehensive treatment of the subject that is both accessible and rigorous, and ultimately deepens our understanding of these important mathematical functions. 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. Nº de ref. del artículo: 9781330209400_0
Comprar nuevo
EUR 15,51
Gastos de envío gratis
Se envía de Reino Unido a Estados Unidos de America
Se envía de Reino Unido a Estados Unidos de America
Cantidad disponible: Más de 20 disponibles
Imagen de archivo
A Contribution to the Theory of Linear Homogeneous Geometric Difference Equations (Q-Difference Equations) (Classic Reprint)
Librería: PBShop.store US, Wood Dale, IL, Estados Unidos de America
Calificación del vendedor: 5 de 5 estrellas
PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781330209400
Comprar nuevo
EUR 24,51
Gastos de envío gratis
Se envía dentro de Estados Unidos de America
Se envía dentro de Estados Unidos de America
Cantidad disponible: 15 disponibles
Imagen de archivo
A Contribution to the Theory of Linear Homogeneous Geometric Difference Equations (Q-Difference Equations) (Classic Reprint)
Librería: PBShop.store UK, Fairford, GLOS, Reino Unido
Calificación del vendedor: 5 de 5 estrellas
PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781330209400
Comprar nuevo
EUR 24,50
Envío por EUR 3,83
Se envía de Reino Unido a Estados Unidos de America
Se envía de Reino Unido a Estados Unidos de America
Cantidad disponible: 15 disponibles