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Functions of Mathematical Physics

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This book is designed to present a rigorous account of the theory of those functions which occur frequently in the study of physics and other sciences. For each function, the theory is developed systematically from the particular definition which has been chosen. Prerequisites for the understanding of the text arc Cauchy's theoren1 and its immediate consequences together with some elementary results on power series and ordinary differential equations.

Author(s): M. G. Smith, Barry Spain
Series: The New university mathematics series
Publisher: Van Nostrand Reinhold
Year: 1970

Language: English
Pages: 220

Preface

CHAPTER 1 SERIES SOLUTION OF SECOND-ORDER LINEAR HOMOGENEOUS EQUATIONS

CHAPTER 2 CONTOUR INTEGRAL SOLUTIONS OF AN ORDINARY LINEAR DIFFERENTIAL EQUATION

CHAPTER 3 OSCILLATION THEOREMS AND STURM-LIOUVILLE THEORY

CHAPTER 4 ASYMPTOTICS

CHAPTER 5 THE GAMMA FUNCTION

CHAPTER 6 THE HYPERGEOMETRIC EQUATION

CHAPTER 7 THE CONFLUENT HYPERGEOMETRIC FUNCTION

CHAPTER 8 THE LEGENDRE FUNCTIONS

CHAPTER 9 BESSEL FUNCTIONS

CHAPTER 10 LAGUERRE POLYNOMIALS

CHAPTER 11 HERMITE POLYNOMIALS

APPENDIX 1 THE LAPLACE AND HELMHOLTZ EQUATIONS

APPENDIX 2 THE SCHRODINGER EQUATION

References

Index