The Table of Integrals, Series, and Products is the essential reference for integrals in the English language. Mathematicians, scientists, and engineers, rely on it when identifying and subsequently solving extremely complex problems. Since publication of the first English-language edition in 1965, it has been thoroughly revised and enlarged on a regular basis, with substantial additions and, where necessary, existing entries corrected or revised.
Author(s): I.S. Gradshteyn and I.M. Ryzhik
Edition: 7th ed
Publisher: Academic Press
Year: 2007
Language: English
Pages: 1221
City: Amsterdam; Boston
Table of Integrals, Series, and Products......Page 4
Copyright page......Page 5
Contents......Page 6
Preface to the Seventh Edition......Page 22
Acknowledgments......Page 24
The Order of Presentation of the Formulas......Page 28
Use of the Tables......Page 32
Index of Special Functions......Page 40
Notation......Page 44
Note on the Bibliographic References......Page 48
0.1 Finite Sums......Page 50
0.2 Numerical Series and Infinite Products......Page 55
0.3 Functional Series......Page 64
0.4 Certain Formulas from Differential Calculus......Page 70
1.1 Power of Binomials......Page 74
1.2 The Exponential Function......Page 75
1.3-1.4 Trigonometric and Hyperbolic Functions......Page 77
1.5 The Logarithm......Page 102
1.6 The Inverse Trigonometric and Hyperbolic Functions......Page 105
2.0 Introduction......Page 112
2.1 Rational Functions......Page 115
2.2 Algebraic Functions......Page 131
2.3 The Exponential Function......Page 155
2.4 Hyperbolic Functions......Page 159
2.5-2.6 Trigonometric Functions......Page 200
2.7 Logarithms and Inverse-Hyperbolic Functions......Page 286
2.8 Inverse Trigonometric Functions......Page 290
3.0 Introduction......Page 296
3.1-3.2 Power and Algebraic Functions......Page 302
3.3-3.4 Exponential Functions......Page 383
3.5 Hyperbolic Functions......Page 420
3.6-4.1 Trigonometric Functions......Page 439
4.2-4.4 Logarithmic Functions......Page 576
4.5 Inverse Trigonometric Functions......Page 648
4.6 Multiple Integrals......Page 656
5.1 Elliptic Integrals and Functions......Page 668
5.2 The Exponential Integral Function......Page 676
5.3 The Sine Integral and the Cosine Integral......Page 677
5.5 Bessel Functions......Page 678
6.1 Elliptic Integrals and Functions......Page 680
6.2-6.3 The Exponential Integral Function and Functions Generated by It......Page 685
6.4 The Gamma Function and Functions Generated by It......Page 699
6.5-6.7 Bessel Functions......Page 708
6.8 Functions Generated by Bessel Functions......Page 802
6.9 Mathieu Functions......Page 812
7.1-7.2 Associated Legendre Functions......Page 818
7.3-7.4 Orthogonal Polynomials......Page 844
7.5 Hypergeometric Functions......Page 861
7.6 Confluent Hypergeometric Functions......Page 869
7.7 Parabolic Cylinder Functions......Page 890
7.8 Meijer's and MacRobert's Functions (G and E)......Page 899
8.1 Elliptic Integrals and Functions......Page 908
8.2 The Exponential Integral Function and Functions Generated by It......Page 932
8.3 Euler's Integrals of the First and Second Kinds......Page 941
8.4-8.5 Bessel Functions and Functions Associated with Them......Page 959
8.6 Mathieu Functions......Page 999
8.7-8.8 Associated Legendre Functions......Page 1007
8.9 Orthogonal Polynomials......Page 1031
9.1 Hypergeometric Functions......Page 1054
9.2 Confluent Hypergeometric Functions......Page 1071
9.3 Meijer's G-Function......Page 1081
9.4 MacRobert's E-Function......Page 1084
9.5 Riemann's Zeta Functions zeta(z,q) and zeta(z), and the Functions Phi(z,s,v) and xi(s)......Page 1085
9.6 Bernoulli Numbers and Polynomials, Euler Numbers......Page 1089
9.7 Constants......Page 1094
10.1-10.8 Vectors, Vector Operators, and Integral Theorems......Page 1098
11.1-11.3 General Algebraic Inequalities......Page 1108
12.11 Mean Value Theorems......Page 1112
12.31 Integral Inequalities......Page 1113
12.51 Fourier Series and Related Inequalities......Page 1115
13.11-13.12 Special Matrices......Page 1118
13.21 Quadratic Forms......Page 1120
13.31 Differentiation of Matrices......Page 1122
13.41 The Matrix Exponential......Page 1123
14.13 Minors and Cofactors of a Determinant......Page 1124
14.16 Jacobi's Theorem......Page 1125
14.21 Cramer's Rule......Page 1126
14.31 Some Special Determinants......Page 1127
15.21 Principal Vector Norms......Page 1130
15.41 Principal Natural Norms......Page 1131
15.51 Spectral Radius of a Square Matrix......Page 1132
15.71 Inequalities for the Characteristic Polynomial......Page 1133
15.81-15.82 Named Theorems on Eigenvalues......Page 1136
15.91 Variational Principles......Page 1140
16.11 First-Order Equations......Page 1142
16.31 First-Order Systems......Page 1143
16.41 Some Special Types of Elementary Differential Equations......Page 1146
16.51 Second-Order Equations......Page 1147
16.61-16.62 Oscillation and Non-Oscillation Theorems for Second-Order Equations......Page 1149
16.81-16.82 Non-Oscillatory Solutions......Page 1152
16.91 Some Growth Estimates for Solutions of Second-Order Equations......Page 1153
16.92 Boundedness Theorems......Page 1155
17.1-17.4 Integral Transforms......Page 1156
18.1-18.3 Definition, Bilateral, and Unilateral z-Transforms......Page 1184
References......Page 1190
Supplemental references......Page 1194
Index of Functions and Constants......Page 1200
General Index of Concepts......Page 1210
