Table of Integrals, Series, and Products
Copyright page
Contents
Preface to the Seventh Edition
Acknowledgments
The Order of Presentation of the Formulas
Use of the Tables
Index of Special Functions
Notation
Note on the Bibliographic References
Chapter 0 Introduction
0.1 Finite Sums
0.2 Numerical Series and Infinite Products
0.3 Functional Series
0.4 Certain Formulas from Differential Calculus
Chapter 1 Elementary Functions
1.1 Power of Binomials
1.2 The Exponential Function
1.3-1.4 Trigonometric and Hyperbolic Functions
1.5 The Logarithm
1.6 The Inverse Trigonometric and Hyperbolic Functions
Chapter 2 Indefinite Integrals of Elementary Functions
2.0 Introduction
2.1 Rational Functions
2.2 Algebraic Functions
2.3 The Exponential Function
2.4 Hyperbolic Functions
2.5-2.6 Trigonometric Functions
2.7 Logarithms and Inverse-Hyperbolic Functions
2.8 Inverse Trigonometric Functions
Chapter 3-4 Definite Integrals of Elementary Functions
3.0 Introduction
3.1-3.2 Power and Algebraic Functions
3.3-3.4 Exponential Functions
3.5 Hyperbolic Functions
3.6-4.1 Trigonometric Functions
4.2-4.4 Logarithmic Functions
4.5 Inverse Trigonometric Functions
4.6 Multiple Integrals
Chapter 5 Indefinite Integrals of Special Functions
5.1 Elliptic Integrals and Functions
5.2 The Exponential Integral Function
5.3 The Sine Integral and the Cosine Integral
5.4 The Probability Integral and Fresnel Integrals
5.5 Bessel Functions
Chapter 6-7 Definite Integrals of Special Functions
6.1 Elliptic Integrals and Functions
6.2-6.3 The Exponential Integral Function and Functions Generated by It
6.4 The Gamma Function and Functions Generated by It
6.5-6.7 Bessel Functions
6.8 Functions Generated by Bessel Functions
6.9 Mathieu Functions
7.1-7.2 Associated Legendre Functions
7.3-7.4 Orthogonal Polynomials
7.5 Hypergeometric Functions
7.6 Confluent Hypergeometric Functions
7.7 Parabolic Cylinder Functions
7.8 Meijer's and MacRobert's Functions (G and E)
Chapter 8-9 Special Functions
8.1 Elliptic Integrals and Functions
8.2 The Exponential Integral Function and Functions Generated by It
8.3 Euler's Integrals of the First and Second Kinds
8.4-8.5 Bessel Functions and Functions Associated with Them
8.6 Mathieu Functions
8.7-8.8 Associated Legendre Functions
8.9 Orthogonal Polynomials
9.1 Hypergeometric Functions
9.2 Confluent Hypergeometric Functions
9.3 Meijer's G-Function
9.4 MacRobert's E-Function
9.5 Riemann's Zeta Functions zeta(z,q) and zeta(z), and the Functions Phi(z,s,v) and xi(s)
9.6 Bernoulli Numbers and Polynomials, Euler Numbers
9.7 Constants
Chapter 10 Vector Field Theory
10.1-10.8 Vectors, Vector Operators, and Integral Theorems
Chapter 11 Algebraic Inequalities
11.1-11.3 General Algebraic Inequalities
Chapter 12 Integral Inequalities
12.11 Mean Value Theorems
12.21 Differentiation of Definite Integral Containing a Parameter
12.31 Integral Inequalities
12.41 Convexity and Jensen's Inequality
12.51 Fourier Series and Related Inequalities
Chapter 13 Matrices and Related Results
13.11-13.12 Special Matrices
13.21 Quadratic Forms
13.31 Differentiation of Matrices
13.41 The Matrix Exponential
Chapter 14 Determinants
14.11 Expansion of Second- and Third-Order Determinants
14.12 Basic Properties
14.13 Minors and Cofactors of a Determinant
14.14 Principal Minors
14.15* Laplace Expansion of a Determinant
14.16 Jacobi's Theorem
14.17 Hadamard's Theorem
14.18 Hadamard's Inequality
14.21 Cramer's Rule
14.31 Some Special Determinants
Chapter 15 Norms
15.1-15.9 Vector Norms
15.11 General Properties
15.21 Principal Vector Norms
15.31 Matrix Norms
15.41 Principal Natural Norms
15.51 Spectral Radius of a Square Matrix
15.61 Inequalities Involving Eigenvalues of Matrices
15.71 Inequalities for the Characteristic Polynomial
15.81-15.82 Named Theorems on Eigenvalues
15.91 Variational Principles
Chapter 16 Ordinary Differential Equations
16.1-16.9 Results Relating to the Solution of Ordinary Differential Equations
16.11 First-Order Equations
16.21 Fundamental Inequalities and Related Results
16.31 First-Order Systems
16.41 Some Special Types of Elementary Differential Equations
16.51 Second-Order Equations
16.61-16.62 Oscillation and Non-Oscillation Theorems for Second-Order Equations
16.71 Two Related Comparison Theorems
16.81-16.82 Non-Oscillatory Solutions
16.91 Some Growth Estimates for Solutions of Second-Order Equations
16.92 Boundedness Theorems
Chapter 17 Fourier, Laplace, and Mellin Transforms
17.1-17.4 Integral Transforms
Chapter 18 The z-Transform
18.1-18.3 Definition, Bilateral, and Unilateral z-Transforms
References
Supplemental references
Index of Functions and Constants
General Index of Concepts