Table of Integrals, Series, and Products / Edition 6

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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. The seventh edition includes a fully searchable CD-Rom.

- Fully searchable CD that puts information at your fingertips included with text
- Most up to date listing of integrals, series and products
- Provides accuracy and efficiency in work

Audience: Professional mathematicians, researchers, engineers, and scientists.

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Editorial Reviews

New edition of a reference that covers integrals and many special functions that arise in all aspects of mathematics and its applications. The tables are organized in a logical manner with standard forms of integrands arranged in increasing order of complexity, ranging from algebraic forms to special functions and combinations. Subsequent chapters deal with the most important special functions and their properties. Edited by Alan Jeffrey (engineering mathematics, U. of Newcastle) and applied mathematician Dan Zwillinger. Annotation c. Book News, Inc., Portland, OR (
From the Publisher
"The integrals are very useful, but this book includes many other features that will be helpful to the reader, especially graduate students. The sections on Hermite and Legendre polynomials are especially helpful for students of Electricity and Magnetism, Quantum Mechanics, and Mathematical physics (they won't have to hunt in several books to find what they need)."
Barry Simon, California Institute of Technology

"This book is to the CRC Mathematical Tables as the unabridged Oxford English Dictionary is to Webster's Collegiate. Besides being big, it's easy to find things in, because of the way the integrals are organized into classes...It really helped me through grad school."
Phil Hobbs, Amazon Review

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Product Details

  • ISBN-13: 9780122947575
  • Publisher: Elsevier Science & Technology Books
  • Publication date: 8/28/2000
  • Edition description: Older Edition
  • Edition number: 6
  • Pages: 1163
  • Product dimensions: 7.92 (w) x 9.62 (h) x 2.32 (d)

Meet the Author

Dr. Daniel Zwillinger is a Senior Principal Systems Engineer for the Raytheon Company. He was a systems requirements “book boss” for the Cobra Judy Replacement (CJR) ship and was a requirements and test lead for tracking on the Ungraded Early Warning Radars (UEWR). He has improved the Zumwalt destroyer’s software accreditation process and he was test lead on an Active Electronically Scanned Array (AESA) radar. Dan is a subject matter expert (SME) in Design for Six Sigma (DFSS) and is a DFSS SME in Test Optimization, Critical Chain Program Management, and Voice of the Customer. He is currently leading a project creating Trust in Autonomous Systems. At Raytheon, he twice won the President’s award for best Six Sigma project of the year: on converting planning packages to work packages for the Patriot missile, and for revising Raytheon’s timecard system. He has managed the Six Sigma white belt training program.
Prior to Raytheon, Dan worked at Sandia Labs, JPL, Exxon, MITRE, IDA, BBN, and The Mathworks (where he developed an early version of their Statistics Toolbox).
For ten years, Zwillinger was owner and president of Aztec Corporation. As a small business, Aztec won several Small Business Innovation Research (SBIR) contracts. The company also created several software packages for publishing companies. Prior to Aztec, Zwillinger was a college professor at Rensselaer Polytechnic Institute in the department of mathematics.
Dan has written several books on mathematics on the topics of differential equations, integration, statistics, and general mathematics. He is editor-in-chief of the Chemical Rubber Company’s (CRC’s) “Standard Mathematical Tables and Formulae”, and is on the editorial board for CRC’s “Handbook of Chemistry and Physics”.
Zwillinger holds a bachelor's degree in mathematics from the Massachusetts Institute of Technology (MIT). He earned his doctorate in applied mathematics from the California Institute of Technology (Caltech). Zwillinger is a certified Raytheon Six Sigma Expert and an ASQ certified Six Sigma Black Belt. He also holds a pilot’s license.

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Table of Contents

Preface to the Sixth Edition xxi
Acknowledgments xxiii
The order of presentation of the formulas xxvii
Use of the tables xxxi
Special functions xxxix
Notation xliii
Note on the bibliographic references xlvii
0 Introduction 1
0.1 Finite sums 1
0.2 Numerical series and infinite products 6
0.3 Functional series 15
0.4 Certain formulas from differential calculus 21
1 Elementary Functions 25
1.1 Power of Binomials 25
1.2 The Exponential Function 26
1.3-1.4 Trigonometric and Hyperbolic Functions 27
1.5 The Logarithm 51
1.6 The Inverse Trigonometric and Hyperbolic Functions 54
2 Indefinite Integrals of Elementary Functions 61
2.0 Introduction 61
2.1 Rational functions 64
2.2 Algebraic functions 80
2.3 The Exponential Function 104
2.4 Hyperbolic Functions 105
2.5-2.6 Trigonometric Functions 147
2.7 Logarithms and Inverse-Hyperbolic Functions 233
2.8 Inverse Trigonometric Functions 237
3-4 Definite Integrals of Elementary Functions 243
3.0 Introduction 243
3.1-3.2 Power and Algebraic Functions 248
3.3-3.4 Exponential Functions 331
3.5 Hyperbolic Functions 365
3.6-4.1 Trigonometric Functions 384
4.2-4.4 Logarithmic Functions 522
4.5 Inverse Trigonometric Functions 596
4.6 Multiple Integrals 604
5 Indefinite Integrals of Special Functions 615
5.1 Elliptic Integrals and Functions 615
5.2 The Exponential Integral Function 622
5.3 The Sine Integral and the Cosine Integral 623
5.4 The Probability Integral and Fresnel Integrals 623
5.5 Bessel Functions 624
6-7 Definite Integrals of Special Functions 625
6.1 Elliptic Integrals and Functions 625
6.2-6.3 The Exponential Integral Function and Functions Generated by It 630
6.4 The Gamma Function and Functions Generated by It 644
6.5-6.7 Bessel Functions 652
6.8 Functions Generated by Bessel Functions 745
6.9 Mathieu Functions 755
7.1-7.2 Associated Legendre Functions 762
7.3-7.4 Orthogonal Polynomials 788
7.5 Hypergeometric Functions 806
7.6 Confluent Hypergeometric Functions 814
7.7 Parabolic Cylinder Functions 835
7.8 Meijer's and MacRobert's Functions (G and E) 843
8-9 Special Functions 851
8.1 Elliptic integrals and functions 851
8.2 The Exponential Integral Function and Functions Generated by It 875
8.3 Euler's Integrals of the First and Second Kinds 883
8.4-8.5 Bessel Functions and Functions Associated with Them 900
8.6 Mathieu Functions 940
8.7-8.8 Associated Legendre Functions 948
8.9 Orthogonal Polynomials 972
9.1 Hypergeometric Functions 995
9.2 Confluent Hypergeometric Functions 1012
9.3 Meijer's G-Function 1022
9.4 MacRobert's E-Function 1025
9.5 Riemann's Zeta Functions [zeta] (z, q), and [zeta] (z), and the Functions [Phi] (z, s, v) and [xi] (s) 1026
9.6 Bernoulli numbers and polynomials, Euler numbers 1030
9.7 Constants 1035
10 Vector Field Theory 1039
10.1-10.8 Vectors, Vector Operators, and Integral Theorems 1039
11 Algebraic Inequalities 1049
11.1-11.3 General Algebraic Inequalities 1049
12 Integral Inequalities 1053
12.11 Mean value theorems 1053
12.21 Differentiation of definite integral containing a parameter 1054
12.31 Integral inequalities 1054
12.41 Convexity and Jensen's inequality 1056
12.51 Fourier series and related inequalities 1056
13 Matrices and related results 1059
13.11-13.12 Special matrices 1059
13.21 Quadratic forms 1061
13.31 Differentiation of matrices 1063
13.41 The matrix exponential 1064
14 Determinants 1065
14.11 Expansion of second- and third-order determinants 1065
14.12 Basic properties 1065
14.13 Minors and cofactors of a determinant 1065
14.14 Principal minors 1066
14.15 Laplace expansion of a determinant 1066
14.16 Jacobi's theorem 1066
14.17 Hadamard's theorem 1066
14.18 Hadamard's inequality 1067
14.21 Cramer's rule 1067
14.31 Some special determinants 1068
15 Norms 1071
15.1-15.9 Vector Norms 1071
15.11 General properties 1071
15.21 Principal vector norms 1071
15.31 Matrix norms 1072
15.41 Principal natural norms 1072
15.51 Spectral radius of a square matrix 1073
15.61 Inequalities involving eigenvalues of matrices 1074
15.71 Inequalities for the characteristic polynomial 1074
15.81-15.82 Named theorems on eigenvalues 1076
15.91 Variational principles 1081
16 Ordinary differential equations 1083
16.1-16.9 Results relating to the solution of ordinary differential equations 1083
16.11 First-order equations 1083
16.21 Fundamental inequalities and related results 1084
16.31 First-order systems 1085
16.41 Some special types of elementary differential equations 1087
16.51 Second-order equations 1088
16.61-16.62 Oscillation and non-oscillation theorems for second-order equations 1090
16.71 Two related comparison theorems 1093
16.81-16.82 Non-oscillatory solutions 1093
16.91 Some growth estimates for solutions of second-order equations 1094
16.92 Boundedness theorems 1096
17 Fourier, Laplace, and Mellin Transforms 1099
17.1-17.4 Integral Transforms 1099
18 The z-transform 1127
18.1-18.3 Definition, Bilateral, and Unilateral z-Transforms 1127
References 1133
Supplemental references 1137
Function and constant index 1143
General index 1153
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