Posted on 2011-08-16. By anonymous.
ÐžlivÐµr & Ð’Ð¾yd | 1956 | ISBN: n/a | 172 pages | PDF | 11 MB
This book is intended for the student of applied Mathematics, physics, chemistry or engineering who wishes to lise the 'special' functions associated with the names of Legendre, Bessel, Hermitc and Lnguerre.
Use is made of only very sparingly and most of the book should be accessible to a reader who has no knowledge of the theory of funclions of a complex variable.
Throughout the text an attempt is made to show how these functions may be used with the problems in classical physics and in quantum theory.
Table of Contents
First Edition 1956
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
Chapter II: Hypergeometric Functions
6. The Hypergeometrlc Series
7. An Integral Formula for the Hypergeometrlc Series.
8. The Hypergeometric Equation
9. Linear Relations between the Solutions of theHypergeometric Equation
10. Relations of Contiguity
11. The ConrJuent 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 Rodriigues
16. Series of Legendre Polynomials
17. Legendre's Differential Equation
18. Neumann's Formula for the Legendre Functions
19. Recurrence Relations for the Function Qn(Âµ).
20. The Usc of Legendre Functions in Potential Theory.
21. Legendre's Associated Functions
22. Integral Expression for the Associated Legendre Function
23. Surface Spherical Harmonics
24. Usc of Associated Legendre Functions in Wave Mechanlcs.
Chspter IV: BESSEL FUNCTIONS
25. The Origin of Bessel Functions
26. Recurrence Relations for the Bessel coefficients
27. Series Expansion for the Bessel Coefficient
28. Integral Expressions for tho BesseI Coefficients
29. The Addilion Formula for Ihe Bessel Coefficients.
30. Bessel's Differential Equation
31. Spherical Bessel Functions
32. Integrals involving Bessel Functons
33. The Modified Bessel Functions
34. The Ber and Bei Functions
35. Expansions in Series of Bessel Functions
36. Thc Use of Bessel Functions in Potcntial Theory
Chapter V: THE FUNCTIONS OF HERMITE AND LAGUERRE
38. The Hermlte Polynomials
39. Hermite's Differential Equatlon
40. Hermite Functions
41. Thc Occurrcncc of Herite Functions in Wave Mechanics
42. The Laguerre Polynomials
43. Laguerre's Differential Equation
44. The Associated Laguerre Polynomials and Functions
45. The Wave Funlctions for the Hydrogen Atom
Appendix: The Dirac Delta Function
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