Difference between revisions of "Book:Ian N. Sneddon/Special Functions of Mathematical Physics and Chemistry"
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=== Contents === | === Contents === | ||
:{{SmallCaps|Preface}} | :{{SmallCaps|Preface}} | ||
− | : | + | : CHAPTER I INTRODUCTION |
::1. The origin of special functions | ::1. The origin of special functions | ||
::2. Ordinary points of a linear differential equation | ::2. Ordinary points of a linear differential equation | ||
Line 12: | Line 12: | ||
::4. The point at infinity | ::4. The point at infinity | ||
::5. The gamma function and related functions | ::5. The gamma function and related functions | ||
− | : | + | : CHAPTER II HYPERGEOMETRIC FUNCTIONS |
::6. The hypergeometric series | ::6. The hypergeometric series | ||
::7. The integral formula for the hypergeometric series | ::7. The integral formula for the hypergeometric series | ||
Line 20: | Line 20: | ||
::11. The confluent hypergeometric function | ::11. The confluent hypergeometric function | ||
::12. Generalised hypergeometric series | ::12. Generalised hypergeometric series | ||
− | : | + | : CHAPTER III LEGENDRE FUNCTIONS |
− | : | + | ::13. Legendre polynomials |
− | : | + | ::14. Recurrence relations for the Legendre polynomials |
+ | ::15. The formulae of Murphy and Rodrigues | ||
+ | ::16. Series of Legendre polynomials | ||
+ | ::17. Legendre's differential equation | ||
+ | ::18. Neumann's formula for the Legendre functions | ||
+ | ::19. Recurrence relations for the function $Q_n(\mu)$ | ||
+ | ::20. The use of Legendre functions in potential theory | ||
+ | ::21. Legendre's associated functions | ||
+ | ::22. Integral expressions for the associated Legendre function | ||
+ | ::23. Surface spherical harmonics | ||
+ | ::24. Use of associated Legendre functions in wave mechanics | ||
+ | : CHAPTER IV BESSEL FUNCTIONS | ||
+ | ::25. The origin of Bessel functions | ||
+ | ::26. Recurrence relations for the Bessel coefficients | ||
+ | ::27. Series expansion for the Bessel coefficients | ||
+ | ::28. Integral expressions for the Bessel coefficients | ||
+ | ::29. The addition formula for the Bessel coefficients | ||
+ | ::30. Bessel's differential equation | ||
+ | ::31. Spherical Bessel Functions | ||
+ | ::32. Integrals involving Bessel functions | ||
+ | ::33. The modified Bessel functions | ||
+ | ::34. The Ber and Bei functions | ||
+ | ::35. Expansions in series of Bessel functions | ||
+ | ::36. The use of Bessel functions in potential theory | ||
+ | ::37. Asymptotic expansions of Bessel functions | ||
+ | : CHAPTER V THE FUNCTIONS OF HERMITE AND LAGUERRE | ||
+ | ::38. The Hermite polynomials | ||
+ | ::39. Hermite's differential equation | ||
+ | ::40. Hermite functions | ||
+ | ::41. The occurence of Hermite functions in wave mechanics | ||
+ | ::42. The Laguerre polynomials | ||
+ | ::43. Laguerre's differential equation | ||
+ | ::44. The associated Laguerre polynomials and functions | ||
+ | ::45. The wave functions for the hydrogen atom | ||
: Appendix: The Dirac Delta Function | : Appendix: The Dirac Delta Function | ||
− | : | + | ::46. The Dirac delta function |
+ | : INDEX | ||
[[Category:Books]] | [[Category:Books]] |
Revision as of 05:17, 6 June 2016
Ian N. Sneddon: Special Functions of Mathematical Physics and Chemistry
Published $1956$, Oliver and Boyd.
Online copies
Contents
- Preface
- CHAPTER I INTRODUCTION
- 1. The origin of special functions
- 2. Ordinary points of a linear differential equation
- 3. Regular singular points
- 4. The point at infinity
- 5. The gamma function and related functions
- CHAPTER II HYPERGEOMETRIC FUNCTIONS
- 6. The hypergeometric series
- 7. The integral formula for the hypergeometric series
- 8. The hypergeometric equation
- 9. Linear relations between the solutions of the hypergeometric equation
- 10. Relations of contiguity
- 11. The confluent hypergeometric function
- 12. Generalised hypergeometric series
- CHAPTER III LEGENDRE FUNCTIONS
- 13. Legendre polynomials
- 14. Recurrence relations for the Legendre polynomials
- 15. The formulae of Murphy and Rodrigues
- 16. Series of Legendre polynomials
- 17. Legendre's differential equation
- 18. Neumann's formula for the Legendre functions
- 19. Recurrence relations for the function $Q_n(\mu)$
- 20. The use of Legendre functions in potential theory
- 21. Legendre's associated functions
- 22. Integral expressions for the associated Legendre function
- 23. Surface spherical harmonics
- 24. Use of associated Legendre functions in wave mechanics
- CHAPTER IV BESSEL FUNCTIONS
- 25. The origin of Bessel functions
- 26. Recurrence relations for the Bessel coefficients
- 27. Series expansion for the Bessel coefficients
- 28. Integral expressions for the Bessel coefficients
- 29. The addition formula for the Bessel coefficients
- 30. Bessel's differential equation
- 31. Spherical Bessel Functions
- 32. Integrals involving Bessel functions
- 33. The modified Bessel functions
- 34. The Ber and Bei functions
- 35. Expansions in series of Bessel functions
- 36. The use of Bessel functions in potential theory
- 37. Asymptotic expansions of Bessel functions
- CHAPTER V THE FUNCTIONS OF HERMITE AND LAGUERRE
- 38. The Hermite polynomials
- 39. Hermite's differential equation
- 40. Hermite functions
- 41. The occurence of Hermite functions in wave mechanics
- 42. The Laguerre polynomials
- 43. Laguerre's differential equation
- 44. The associated Laguerre polynomials and functions
- 45. The wave functions for the hydrogen atom
- Appendix: The Dirac Delta Function
- 46. The Dirac delta function
- INDEX