A Contribution to the Theory of Linear Homogeneous Geometric Difference

Folke Ryde

ISBN 10: 1330209400 / ISBN 13: 9781330209400

Published by Forgotten Books, 2018

About this Item

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.

Seller Inventory # 9781330209400_0

Bibliographic Details

• Title: A Contribution to the Theory of Linear Homogeneous Geometric Difference
• Publisher: Forgotten Books
• Publication Date: 2018
• Language: English
• ISBN 10: 1330209400
• ISBN 13: 9781330209400
• Binding: Paperback
• Condition: New
• Book Type: print-on-demand item
• Seller catalogs:
  • Calculus

About this title

Synopsis

A rigorous study of geometric factorial series and q-difference equations, this work develops methods to construct and analyze solutions to linear homogeneous equations in a multiplicatively scaled setting.

It surveys main properties, proves existence and linear independence of solution systems, and links the results to classical theories in the field.

• Learn how geometric factorial series are defined, convergent, and represented in holomorphic form.
• See how a fundamental system of solutions is built and shown to be linearly independent.
• Explore the asymptotic behavior and analytic character of solutions, including connections to known results by Frobenius, Norlund, and Heine.
• Discover applications to particular equations and how these methods relate to q-calculus and related differential analogues.

Ideal for readers of advanced mathematics and researchers in difference equations and special functions.