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Revision as of 05:45, 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
