Difference between revisions of "Book:Ian N. Sneddon/Special Functions of Mathematical Physics and Chemistry"
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{{Book|Special Functions of Mathematical Physics and Chemistry|1956|Oliver and Boyd||Ian N. Sneddon}} | {{Book|Special Functions of Mathematical Physics and Chemistry|1956|Oliver and Boyd||Ian N. Sneddon}} | ||
− | === | + | ===Online copies=== |
− | + | [https://archive.org/details/SpecialFunctionsOfMathematicalPhysicsAndChemistry hosted by archive.org] | |
− | |||
− | |||
=== Contents === | === Contents === | ||
− | + | :{{SmallCaps|Preface}} | |
− | : {{SmallCaps|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 | |
− | : | + | :::[[Gamma|$(5.1)$]] |
− | + | :::[[Beta|$(5.2)$]] | |
− | : | + | :::-------------- |
− | + | :::[[Cosine integral|$(5.10)$]] (and [[Sine integral|$(5.10)$]]) | |
− | : | + | :::[[Error function|$(5.11)$]] |
− | + | : 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 | ||
+ | :::---------- | ||
+ | :::[[Hypergeometric pFq|$(12.4)$]] | ||
+ | : 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:Book]] | |
− | |||
− | [[Category: |
Latest revision as of 03:07, 25 June 2017
Ian N. Sneddon: Special Functions of Mathematical Physics and Chemistry
Published $1956$, Oliver and Boyd.
Online copies
Contents
- Preface
- CHAPTER I INTRODUCTION
- 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
- ----------
- $(12.4)$
- 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