# "Special Functions of Mathematical Physics and Chemistry (LMT)" by Ian N. Sneddon

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Posted on 2011-08-16. By anonymous.

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**"Special Functions of Mathematical Physics and Chemistry (LMT)" by Ian N. Sneddon**

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

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

Exercises

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

Examples

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.

Examples

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

Examples

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

Examples

Appendix: The Dirac Delta Function

INDEX

with TOC BookMarkLinks

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