View source for Book:Arthur Erdélyi/Higher Transcendental Functions Volume II

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{{Book|Higher Transcendental Functions, Volume II|1953|Dover Publications|0-486-44614-X|Harry Bateman}}

===Online mirrors===
[http://authors.library.caltech.edu/43491/ hosted by Caltech]<br />

===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
:::::(1)
:::::[[Bessel J|(2)]]
:::::(3)
:::::(4)
:::::(5)
:::::(6)
:::::(7)
:::::(8)
:::::(9)
:::::(10)
::::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
:CHAPTER VIII FUNCTIONS OF THE PARABOLIC CYLINDER AND OF THE PARABOLOID OF REVOLUTION
:::8.1. Introduction
::PARABOLIC CYLINDER FUNCTIONS
:::8.2. Definitions and elementary properties
:::8.3. Integral representations and integrals
:::8.4. Asymptotic expansions
:::8.5 Representation of functions in terms of the $D_{\nu}(x)$
::::8.5.1. Series
::::8.5.2. Representation by integrals with respect to the parameter
:::8.6 Zeros and descriptive properties
::FUNCTIONS OF THE PARABOLOID OF REVOLUTION
:::8.7 The solutions of a particular confluent hypergeometric equation
:::8.8 Integrals and series involving functions of the paraboloid of revolution
:CHAPTER IX THE INCOMPLETE GAMMA FUNCTIONS AND RELATED FUNCTIONS
:::9.1. Introduction
::THE INCOMPLETE GAMMA FUNCTIONS
:::9.2. Definitions and elementary properties
::::9.2.1. The case of integer $a$
:::9.3. Integral representations and integral formulas
:::9.4. Series
:::9.5. Asymptotic representations
:::9.6. Zeros and descriptive properties
::SPECIAL INCOMPLETE GAMMA FUNCTIONS
:::9.7. The exponential and logarithmic integral
:::9.8. Sine and cosine integrals
:::9.9. The error functions
:::9.10. Fresenel integrals and generalizations
:::References
:CHAPTER X ORTHOGONAL POLYNOMIALS
:::10.1. Systems of orthogonal functions
:::10.2. The approximation problem
:::10.3. General properties of orthogonal polynomials
:::10.4. Mechanical quadrature
:::10.5. Continued fractions
:::10.6. The classical polynomials
:::10.7. General properties of the classical orthogonal polynomials
:::10.8. Jacobi polynomials
:::10.9. Gegenbauer polynomials
:::10.10. Legendre polynomials
:::10.11. Tchebichef polynomials
:::10.12. Laguerre polynomials
:::10.13. Hermite polynomials
:::10.14. Asymptotic behavior of Jacobi, Gegenbauer and Legendre polynomials
:::10.15. Zeros of Jacobi and related polynomials
:::10.16. Zeros of Laguerre and Hermite polynomials
:::10.17. Zeros of Laguerre and Hermite polynomials
:::10.18. Inequalities for the classical polynomials
:::10.19. Expansion problems
:::10.20. Examples of expansions
:::10.21. Some classes of orthogonal polynomials
:::10.22. Orthogonal polynomials of a discrete variable
:::10.23. Tchebichef's polynomials of a discrete variable and their generalizations
:::10.24. Krawtchouk's and related polynomials
:::10.25 Charlier's polynomials
:::References

===See also===
[[Book:Harry Bateman/Higher Transcendental Functions Volume I]]<br />
[[Book:Harry Bateman/Higher Transcendental Functions Volume III]]<br />

[[Category:Book]]