Difference between revisions of "Book:Arthur Erdélyi/Higher Transcendental Functions Volume II"
From specialfunctionswiki
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===Contents=== | ===Contents=== | ||
:FOREWARD | :FOREWARD | ||
| − | :CHAPTER VII BESSEL FUNCTIONS FIRST PART: THEORY | + | :CHAPTER VII |
| − | ::7.1. Introduction | + | ::BESSEL FUNCTIONS FIRST PART: THEORY |
| − | ::7.2. Bessel's differential equation | + | :::7.1. Introduction |
| − | :::7.2.1. Bessel functions of general order | + | :::7.2. Bessel's differential equation |
| − | :::7.2.3. Kelvin's function and related functions | + | ::::7.2.1. Bessel functions of general order |
| − | :::7.2.4. Bessel functions of integer order | + | ::::7.2.3. Kelvin's function and related functions |
| − | :::7.2.5. Modified Bessel functions of integer order | + | ::::7.2.4. Bessel functions of integer order |
| − | :::7.2.6. Spherical Bessel functions | + | ::::7.2.5. Modified Bessel functions of integer order |
| − | :::7.2.7. Products of Bessel functions | + | ::::7.2.6. Spherical Bessel functions |
| − | :::7.2.8. Miscellaneous results | + | ::::7.2.7. Products of Bessel functions |
| − | ::7.3. Integral representations | + | ::::7.2.8. Miscellaneous results |
| − | :::7.3.1. Bessel coefficients | + | :::7.3. Integral representations |
| − | :::7.3.2. Integral representations of the Poisson type | + | ::::7.3.1. Bessel coefficients |
| − | :::7.3.3. Representations by loop integrals | + | ::::7.3.2. Integral representations of the Poisson type |
| − | :::7.3.4. Shläfli's, Gubler's, Sonine's and related integrals | + | ::::7.3.3. Representations by loop integrals |
| − | :::7.3.5. Sommerfeld's integrals | + | ::::7.3.4. Shläfli's, Gubler's, Sonine's and related integrals |
| − | :::7.3.6. Barnes' integrals | + | ::::7.3.5. Sommerfeld's integrals |
| − | :::7.3.7. Airy's integrals | + | ::::7.3.6. Barnes' integrals |
| − | ::7.4. Asymptotic expansions | + | ::::7.3.7. Airy's integrals |
| − | :::7.4.1. Large variable | + | :::7.4. Asymptotic expansions |
| − | :::7.4.2. Large order | + | ::::7.4.1. Large variable |
| − | :::7.4.3. Transitional regions | + | ::::7.4.2. Large order |
| − | :::7.4.4. Uniform asymptotic expansions | + | ::::7.4.3. Transitional regions |
| − | ::7.5. Related functions | + | ::::7.4.4. Uniform asymptotic expansions |
| − | :::7.5.1. Neumann's and related polynomials | + | :::7.5. Related functions |
| − | :::7.5.2. Lommel's poylnomials | + | ::::7.5.1. Neumann's and related polynomials |
| − | :::7.5.3. Anger-Weber functions | + | ::::7.5.2. Lommel's poylnomials |
| − | :::7.5.4. Struves' functions | + | ::::7.5.3. Anger-Weber functions |
| − | :::7.5.5. Lommel's functions | + | ::::7.5.4. Struves' functions |
| − | :::7.5.6. Some other notations and related functions | + | ::::7.5.5. Lommel's functions |
| − | ::7.6. Addition theorems | + | ::::7.5.6. Some other notations and related functions |
| − | :::7.6.1. Gegenbauer's addition theorem | + | :::7.6. Addition theorems |
| − | :::7.6.2. Graf's addition theorem | + | ::::7.6.1. Gegenbauer's addition theorem |
| − | ::7.7. Integral formulas | + | ::::7.6.2. Graf's addition theorem |
| − | :::7.7.1. Indefinite integrals | + | :::7.7. Integral formulas |
| − | :::7.7.2. Finite integrals | + | ::::7.7.1. Indefinite integrals |
| − | :::7.7.3. Infinite integrals with exponential functions | + | ::::7.7.2. Finite integrals |
| − | :::7.7.4. The discontinuous integral of Weber and Schafheitlin | + | ::::7.7.3. Infinite integrals with exponential functions |
| − | :::7.7.5. Sonine and Gegenbauer's integrals and generalizations | + | ::::7.7.4. The discontinuous integral of Weber and Schafheitlin |
| − | :::7.7.6. Macdonald's and Nicholson's formulas | + | ::::7.7.5. Sonine and Gegenbauer's integrals and generalizations |
| − | :::7.7.7. Integrals with respect to order | + | ::::7.7.6. Macdonald's and Nicholson's formulas |
| − | ::7.8. Relations between Bessel and Legendre functions | + | ::::7.7.7. Integrals with respect to order |
| − | ::7.9. Zeros of the Bessel functions | + | :::7.8. Relations between Bessel and Legendre functions |
| − | ::7.10. Series and integral representations of arbitrary functions | + | :::7.9. Zeros of the Bessel functions |
| − | :::7.10.1. Neumann's series | + | :::7.10. Series and integral representations of arbitrary functions |
| − | :::7.10.2. Kapteyn series | + | ::::7.10.1. Neumann's series |
| − | :::7.10.3. Schlömilch series | + | ::::7.10.2. Kapteyn series |
| − | :::7.10.4. Fourier-Bessel and Dini series | + | ::::7.10.3. Schlömilch series |
| − | :::7.10.5. Integral representations of arbitrary functions | + | ::::7.10.4. Fourier-Bessel and Dini series |
| − | :SECOND PART: FORMULAS | + | ::::7.10.5. Integral representations of arbitrary functions |
| − | ::7.11. Elementary relations and miscellaneous formulas | + | ::SECOND PART: FORMULAS |
| − | ::7.12. Integral representations | + | :::7.11. Elementary relations and miscellaneous formulas |
| − | ::7.13. Asymptotic expansions | + | :::7.12. Integral representations |
| − | :::7.13.1. Large variable | + | :::7.13. Asymptotic expansions |
| − | :::7.13.2. Large order | + | ::::7.13.1. Large variable |
| − | :::7.13.3. Transitional regions | + | ::::7.13.2. Large order |
| − | :::7.13.4. Uniform asymptotic expansions | + | ::::7.13.3. Transitional regions |
| − | ::7.14. Integral formulas | + | ::::7.13.4. Uniform asymptotic expansions |
| − | :::7.14.1. Finite integrals | + | :::7.14. Integral formulas |
| − | :::7.14.2. Infinite integrals | + | ::::7.14.1. Finite integrals |
| − | ::7.15. Series of Bessel functions | + | ::::7.14.2. Infinite integrals |
| − | ::References | + | :::7.15. Series of Bessel functions |
| + | :::References | ||
[[Category:Books]] | [[Category:Books]] | ||
Revision as of 05:52, 5 June 2016
Harry Bateman: Higher Transcendental Functions, Volume I
Published $1953$, Dover Publications
- ISBN 0-486-44614-X.
Online mirrors
Contents
- FOREWARD
- CHAPTER VII
- BESSEL FUNCTIONS FIRST PART: THEORY
- 7.1. Introduction
- 7.2. Bessel's differential equation
- 7.2.1. Bessel functions of general order
- 7.2.3. Kelvin's function and related functions
- 7.2.4. Bessel functions of integer order
- 7.2.5. Modified Bessel functions of integer order
- 7.2.6. Spherical Bessel functions
- 7.2.7. Products of Bessel functions
- 7.2.8. Miscellaneous results
- 7.3. Integral representations
- 7.3.1. Bessel coefficients
- 7.3.2. Integral representations of the Poisson type
- 7.3.3. Representations by loop integrals
- 7.3.4. Shläfli's, Gubler's, Sonine's and related integrals
- 7.3.5. Sommerfeld's integrals
- 7.3.6. Barnes' integrals
- 7.3.7. Airy's integrals
- 7.4. Asymptotic expansions
- 7.4.1. Large variable
- 7.4.2. Large order
- 7.4.3. Transitional regions
- 7.4.4. Uniform asymptotic expansions
- 7.5. Related functions
- 7.5.1. Neumann's and related polynomials
- 7.5.2. Lommel's poylnomials
- 7.5.3. Anger-Weber functions
- 7.5.4. Struves' functions
- 7.5.5. Lommel's functions
- 7.5.6. Some other notations and related functions
- 7.6. Addition theorems
- 7.6.1. Gegenbauer's addition theorem
- 7.6.2. Graf's addition theorem
- 7.7. Integral formulas
- 7.7.1. Indefinite integrals
- 7.7.2. Finite integrals
- 7.7.3. Infinite integrals with exponential functions
- 7.7.4. The discontinuous integral of Weber and Schafheitlin
- 7.7.5. Sonine and Gegenbauer's integrals and generalizations
- 7.7.6. Macdonald's and Nicholson's formulas
- 7.7.7. Integrals with respect to order
- 7.8. Relations between Bessel and Legendre functions
- 7.9. Zeros of the Bessel functions
- 7.10. Series and integral representations of arbitrary functions
- 7.10.1. Neumann's series
- 7.10.2. Kapteyn series
- 7.10.3. Schlömilch series
- 7.10.4. Fourier-Bessel and Dini series
- 7.10.5. Integral representations of arbitrary functions
- SECOND PART: FORMULAS
- 7.11. Elementary relations and miscellaneous formulas
- 7.12. Integral representations
- 7.13. Asymptotic expansions
- 7.13.1. Large variable
- 7.13.2. Large order
- 7.13.3. Transitional regions
- 7.13.4. Uniform asymptotic expansions
- 7.14. Integral formulas
- 7.14.1. Finite integrals
- 7.14.2. Infinite integrals
- 7.15. Series of Bessel functions
- References
- BESSEL FUNCTIONS FIRST PART: THEORY
