Difference between revisions of "Book:Arthur Erdélyi/Higher Transcendental Functions Volume III"

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(Created page with "__NOTOC__ {{Book|Higher Transcendental Functions, Volume III|1953|Dover Publications|0-486-44614-X|Harry Bateman}} ===Online mirrors=== [http://authors.library.caltech.edu/4...")
 
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===Online mirrors===
 
===Online mirrors===
 
[http://authors.library.caltech.edu/43491/ hosted by Caltech]<br />
 
[http://authors.library.caltech.edu/43491/ hosted by Caltech]<br />
 +
 +
===Contents===
 +
:CONTENTS
 +
::FOREWORD
 +
:CHAPTER XIV AUTOMORPHIC FUNCTIONS
 +
:::14.1. Discontinuous groups and homographic transformations
 +
::::14.1.1. Homographic transformations
 +
::::14.1.2. Fixed points. Classification of transformations
 +
::::14.1.3. Discontinuous groups
 +
::::14.1.4. Fundamental region
 +
:::14.2. Definition of automorphic functions
 +
:::14.3. The icosahedral group
 +
:::14.4. Parabolic substitutions
 +
:::14.5. Infinite cyclic group with two fixed points
 +
:::14.6. Elliptic modular functions
 +
::::14.6.1. The modular group
 +
::::14.6.2. The modular function $\mathcal{J}(z)$
 +
::::14.6.3. Subgroups of the modular group
 +
::::14.6.4. Modular equations
 +
::::14.6.5. Applications to number theory
 +
:::14.7. General theory of automorphic functions
 +
::::14.7.1. Classification of the groups
 +
::::14.7.2. General theorems on automorphic functions
 +
:::14.8. Existence and construction of automorphic functions
 +
::::14.8.1. General remarks
 +
::::14.8.2. Riemann surfaces
 +
::::14.8.3. Automorphic forms, Poincaré's theta series
 +
:::14.9. Uniformization
 +
:::14.10. Special automorphic functions
 +
::::14.10.1. The Riemann-Schwarz triangle functions
 +
::::14.10.2. Burnside's automorphic functions
 +
:::14.11. Hilbert's modular groups
 +
:::14.12. Siegel's functions
 +
:::References
 +
:CHAPTER XV LAMÉ FUNCTIONS
 +
:::15.1. Introduction
 +
::::15.1.1. Coordinates of confocal quadrics
 +
::::15.1.2. Coordinates of confocal cones
 +
::::15.1.3. Coordinates of confocal cyclides of revolution
 +
:::15.2. Lamé-Wangerin functions
 +
:::15.3. Heun's equation
 +
:::15.4. Solutions of the general Lamé equation
 +
:::15.5. Lamé functions
 +
::::15.5.1. Lamé functions of real periods
 +
::::15.5.2. Lamé functions of imaginary periods. Transformation formulas
 +
::::15.5.3. Integral equations for Lamé functions
 +
::::15.5.4. Degenerate cases
 +
:::15.6. Lamé-Wangerin functions
 +
:::15.7. Ellipsoidal and sphero-conal harmonics
 +
:::15.8. Harmonics associated with cyclides of revolution
 +
:::References
 +
:CHAPTER XVI MATHIEU FUNCTIONS, SPHEROIDAL AND ELLIPSOIDAL WAVE FUNCTIONS
 +
:::16.1.
 +
  
 
===See also===
 
===See also===

Revision as of 06:17, 5 June 2016


Harry Bateman: Higher Transcendental Functions, Volume III

Published $1953$, Dover Publications

ISBN 0-486-44614-X.


Online mirrors

hosted by Caltech

Contents

CONTENTS
FOREWORD
CHAPTER XIV AUTOMORPHIC FUNCTIONS
14.1. Discontinuous groups and homographic transformations
14.1.1. Homographic transformations
14.1.2. Fixed points. Classification of transformations
14.1.3. Discontinuous groups
14.1.4. Fundamental region
14.2. Definition of automorphic functions
14.3. The icosahedral group
14.4. Parabolic substitutions
14.5. Infinite cyclic group with two fixed points
14.6. Elliptic modular functions
14.6.1. The modular group
14.6.2. The modular function $\mathcal{J}(z)$
14.6.3. Subgroups of the modular group
14.6.4. Modular equations
14.6.5. Applications to number theory
14.7. General theory of automorphic functions
14.7.1. Classification of the groups
14.7.2. General theorems on automorphic functions
14.8. Existence and construction of automorphic functions
14.8.1. General remarks
14.8.2. Riemann surfaces
14.8.3. Automorphic forms, Poincaré's theta series
14.9. Uniformization
14.10. Special automorphic functions
14.10.1. The Riemann-Schwarz triangle functions
14.10.2. Burnside's automorphic functions
14.11. Hilbert's modular groups
14.12. Siegel's functions
References
CHAPTER XV LAMÉ FUNCTIONS
15.1. Introduction
15.1.1. Coordinates of confocal quadrics
15.1.2. Coordinates of confocal cones
15.1.3. Coordinates of confocal cyclides of revolution
15.2. Lamé-Wangerin functions
15.3. Heun's equation
15.4. Solutions of the general Lamé equation
15.5. Lamé functions
15.5.1. Lamé functions of real periods
15.5.2. Lamé functions of imaginary periods. Transformation formulas
15.5.3. Integral equations for Lamé functions
15.5.4. Degenerate cases
15.6. Lamé-Wangerin functions
15.7. Ellipsoidal and sphero-conal harmonics
15.8. Harmonics associated with cyclides of revolution
References
CHAPTER XVI MATHIEU FUNCTIONS, SPHEROIDAL AND ELLIPSOIDAL WAVE FUNCTIONS
16.1.


See also

Book:Harry Bateman/Higher Transcendental Functions Volume I
Book:Harry Bateman/Higher Transcendental Functions Volume II

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