Heun's Differential Equations by A. RonveauxHeun's Differential Equations by A. Ronveaux

Heun's Differential Equations

byA. Ronveaux

Hardcover | April 30, 1999

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Heun's equation is a second-order differential equation which crops up in a variety of forms in a wide range of problems in applied mathematics. These include integral equations of potential theory, wave propogation, electrostatic oscillation, and Schrodinger's equation. This volume bringstogether important research work for the first time, providing an important resource for all those interested in this mathematical topic. Both the current theory and the main areas of application are surveyed, and includes contributions from authoritative researchers such as Felix Arscott (Canada),P. Maroni (France), and Gerhard Wolf (Germany).
A. Ronveaux is at Facultes Universitaires Notre Dame de la Paix, Namur.
Title:Heun's Differential EquationsFormat:HardcoverDimensions:380 pages, 9.21 × 6.14 × 0.98 inPublished:April 30, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198596952

ISBN - 13:9780198596950

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Table of Contents

PrefaceIntroductionA. Heun's Equation1. General features of Heun's equation2. Transformations of Heun's equation3. Solutions of Heun's equationI: General and power series4. Solution of Heun's equationII: Hypergeometric function series5. Orthogonality relations6. Integral equations and integral relationsAppendixB. Confluent Heun Equation1. General features of the confluent Heun equation2. Solution of the confluent Heun equation3. Confluent Heun functions4. Asymptotic expansions5. ReferencesC. Double Confluent Heun Equation1. General features of the DCHE2. The analytic theory of the DCHE3. Special results4. ReferencesD. Biconfluent Heun Equation1. General features of BHE equation2. Transformers of BHE equation3. Solutions of the BHE equation4. Integral relations5. Miscellaneous6. ReferencesE. Triconfluent Heun Equation1. General features of the THE equation2. Transformations of the THE equation3. Solutions of particular THE equations4. Solutions in the vicinity of the singularity5. Asymptotics with respect to a parameter6. ReferencesAddendum: Clssification1. Linear differential equations of second order with polynomial coefficients2. The classification scheme3. Confluence Theorems4. Tables5. ReferencesBibliographyAuthor and Subject Index

Editorial Reviews

`There is a wealth of important results and open problems and the book is a welcome addition to the literature on these important special functions and their applications.'B D Sleeman, Zbl. Math. 847/96.