Book:Ian N. Sneddon/Special Functions of Mathematical Physics and Chemistry/Second Edition
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Ian N. Sneddon: Special Functions of Mathematical Physics and Chemistry (2nd Edition)
Published $\text {1961}$, Oliver and Boyd
Subject Matter
Contents
- Preface
- chapter $\text {I}$: 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
- Examples $\text {I}$
- chapter $\text {II}$: HYPERGEOMETRIC FUNCTIONS
- 6. The hypergeometric series
- 7. An 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
- Examples $\text {II}$
- chapter $\text {III}$: LEGENDRE FUNCTIONS
- 13. Legendre polynomials
- 14. Recurrence relations for the Legendre polynomial
- 15. The formulae of Murphy and Rodrigues
- 16. Series of Legendre polynomials
- 17. Legendre's difference equation
- 18. Neumann's formula for the Legendre functions
- 19. Recurrence relations for the function $\map {Q_n} \mu$
- 20. The use of Legendre functions in potential theory
- 21. Legendre's associated functions
- 22. Integral expression for the associated Legendre function
- 23. Surface spherical harmonics
- 24. Use of associated Legendre functions in wave mechanics
- Examples $\text {III}$
- chapter $\text {IV}$: 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
- Examples $\text {IV}$
- chapter $\text {V}$: THE FUNCTIONS OF HERMITE AND LAGUERRE
- 38. The Hermite polynomials
- 39. Hermite's differential equation
- 40. Hermite functions
- 41. The occurrence 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
- Examples $\text {V}$
- appendix: THE DIRAC DELTA FUNCTION
- 46. The Dirac delta function
- INDEX
Further Editions
Source work progress
- 1961: Ian N. Sneddon: Special Functions of Mathematical Physics and Chemistry (2nd ed.) ... (previous) ... (next): Chapter $\text I$: Introduction: $\S 1$. The origin of special functions: $(1.5)$