Difference between revisions of "Book:Arthur Erdélyi/Higher Transcendental Functions Volume III"
From specialfunctionswiki
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:::16.8. Series, integrals, and expansion problems | :::16.8. Series, integrals, and expansion problems | ||
::SPHEROIDAL WAVE FUNCTIONS | ::SPHEROIDAL WAVE FUNCTIONS | ||
| − | :::16.9. | + | :::16.9. The differential equation of spheroidal wave functions and its solution |
| − | :::16.10. | + | :::16.10. Further expansions, approximations, integral relations |
| − | :::16.11. | + | :::16.11. Spheroidal wave functions |
| − | :::16.12. | + | :::16.12. Approximations and asymptotic forms for spheroidal wave functions |
| − | :::16.13. | + | :::16.13. Series and integrals involving spheroidal wave functions |
| − | :::16.14. | + | ::ELLIPSOIDAL WAVE FUNCTIONS |
| + | :::16.14. Lamé's wave equation | ||
| + | :::References | ||
Revision as of 06:21, 5 June 2016
Harry Bateman: Higher Transcendental Functions, Volume III
Published $1953$, Dover Publications
- ISBN 0-486-44614-X.
Online mirrors
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
- 14.1. Discontinuous groups and homographic transformations
- 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
- 15.1. Introduction
- CHAPTER XVI MATHIEU FUNCTIONS, SPHEROIDAL AND ELLIPSOIDAL WAVE FUNCTIONS
- 16.1. Introduction
- 16.2. The general Mathieu equation and its solutions
- 16.3. Approximations, integral relations, and integral equations for solutions of the general Mathieu equation
- 16.4. Periodic Mathieu functions
- 16.5. Expansions of Mathieu functions and functions of the second kind
- 16.6. Modified Mathieu functions
- 16.7. Approximations and asymptotic forms
- 16.8. Series, integrals, and expansion problems
- SPHEROIDAL WAVE FUNCTIONS
- 16.9. The differential equation of spheroidal wave functions and its solution
- 16.10. Further expansions, approximations, integral relations
- 16.11. Spheroidal wave functions
- 16.12. Approximations and asymptotic forms for spheroidal wave functions
- 16.13. Series and integrals involving spheroidal wave functions
- ELLIPSOIDAL WAVE FUNCTIONS
- 16.14. Lamé's wave equation
- References
See also
Book:Harry Bateman/Higher Transcendental Functions Volume I
Book:Harry Bateman/Higher Transcendental Functions Volume II
