The Functions of Mathematical Physics by Hochstadt, Harry -- Read -- Imperial Library of Trantor

Index

Cover Title Page Copyright Page Foreword Preface Contents 1 Orthogonal Polynomials

1 Linear Spaces 2 Orthogonal Polynomials 3 The Recurrence Formula 4 The Christoffel—Darboux Formula 5 The Weierstrass Approximation Theorem 6 The Zeros of the Orthogonal Polynomials 7 Approximation Theory 8 More about the Zeros of the Orthonormal Polynomials 9 The completeness of the Orthonormal Polynomials in the Space of Square-Integrable Functions 10 Generalizations and an Application to Conformal Mappings

2 The Classical Orthogonal Polynomials

3 The Gamma Function

1 Definitions and Basic Properties 2 Analytic Continuation and Integral Representations 3 Asymptotic Expansions 4 Beta Functions 5 The Logarithmic Derivative of the Gamma Function 6 Mellin-Barnes Integrals 7 Mellin Transforms 8 Applications to Algebraic Equations

4 Hypergeometric Functions

5 The Legendre Functions

1 Laplace's Differential Equation 2 Maxwell's Theory of Poles 3 Relationship to the Hypergeometric Functions 4 Expansion Formulas 5 The Addition Theorem 6 Green's Functions 7 The Complete Solution of Legendre's Differential Equation 8 Asymptotic Formulas

6 Spherical Harmonics in p Dimensions

1 Homogeneous Polynomials 2 Orthogonality of Spherical Harmonics 3 Legendre Polynomials 4 Applications to Boundary Value Problems

7 Confluent Hypergeometric Functions

1 Relationship to the Hypergeometric Functions 2 Applications of These Functions in Mathematical Physics 3 Integral Representations 4 Asymptotic Representations

8 Bessel Functions

1 Basic Definitions 2 Integral Representations 3 Relationship to the Legendre Functions 4 The Generating Function of the Bessel Function 5 More Integral Representations 6 Addition Theorems 7 The Complete Solution of Bessel's Equation 8 Asymptotic Expansions for Large Argument 9 Airy Functions 10 Asymptotic Expansions for Large Indices and Large Arguments 11 Some Applications of Bessel Functions in Physical Optics 12 The Zeros of Bessel Functions 13 Fourier-Bessel Expansions 14 Applications in Mathematical Physics 15 Discontinuous Integrals

9 Hill's Equation

1 Mathieu's Equation 2 Hill's Equation 3 The Discriminant 4 Expansion Theorems 5 Inverse Problems 6 Hill's Equations with Even Coefficients 7 Mathieu's Equation Revisited 8 Energy Bands in Crystals Appendix

Bibliography Index