Elsevier S & T

Table of Integrals, Series, and Products

Jeffrey, Alan; Zwillinger, Daniel

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Table of contents
  • Front CoverCover
  • Table of Integrals, Series, and Productsiii
  • Copyright Pageiv
  • Contentsv
  • Preface to the Seventh Editionxxi
  • Acknowledgmentsxxiii
  • The Order of Presentation of the Formulasxxvii
  • Use of the Tablesxxxi
  • Index of Special Functionsxxxix
  • Notationxliii
  • Note on the Bibliographic Referencesxlvii
  • Chapter 0 Introduction1
  • 0.1 Finite Sums1
  • 0.2 Numerical Series and Infinite Products6
  • 0.3 Functional Series15
  • 0.4 Certain Formulas from Differential Calculus21
  • Chapter 1 Elementary Functions25
  • 1.1 Power of Binomials25
  • 1.2 The Exponential Function26
  • 1.3-1.4 Trigonometric and Hyperbolic Functions28
  • 1.5 The Logarithm53
  • 1.6 The Inverse Trigonometric and Hyperbolic Functions56
  • Chapter 2 Indefinite Integrals of Elementary Functions63
  • 2.0 Introduction63
  • 2.1 Rational Functions66
  • 2.2 Algebraic Functions82
  • 2.3 The Exponential Function106
  • 2.4 Hyperbolic Functions110
  • 2.5-2.6 Trigonometric Functions151
  • 2.7 Logarithms and Inverse-Hyperbolic Functions237
  • 2.8 Inverse Trigonometric Functions241
  • Chapter 3-4 Definite Integrals of Elementary Functions247
  • 3.0 Introduction247
  • 3.1-3.2 Power and Algebraic Functions253
  • 3.3-3.4 Exponential Functions334
  • 3.5 Hyperbolic Functions371
  • 3.6-4.1 Trigonometric Functions390
  • 4.2-4.4 Logarithmic Functions527
  • 4.5 Inverse Trigonometric Functions599
  • 4.6 Multiple Integrals607
  • Chapter 5 Indefinite Integrals of Special Functions619
  • 5.1 Elliptic Integrals and Functions619
  • 5.2 The Exponential Integral Function627
  • 5.3 The Sine Integral and the Cosine Integral628
  • 5.4 The Probability Integral and Fresnel Integrals629
  • 5.5 Bessel Functions629
  • Chapter 6-7 Definite Integrals of Special Functions631
  • 6.1 Elliptic Integrals and Functions631
  • 6.2-6.3 The Exponential Integral Function and Functions Generated by It636
  • 6.4 The Gamma Function and Functions Generated by It650
  • 6.5-6.7 Bessel Functions659
  • 6.8 Functions Generated by Bessel Functions753
  • 6.9 Mathieu Functions763
  • 7.1-7.2 Associated Legendre Functions769
  • 7.3-7.4 Orthogonal Polynomials795
  • 7.5 Hypergeometric Functions812
  • 7.6 Confluent Hypergeometric Functions820
  • 7.7 Parabolic Cylinder Functions841
  • 7.8 Meijer's and MacRobert's Functions (G and E)850
  • Chapter 8-9 Special Functions859
  • 8.1 Elliptic Integrals and Functions859
  • 8.2 The Exponential Integral Function and Functions Generated by It883
  • 8.3 Euler's Integrals of the First and Second Kinds892
  • 8.4-8.5 Bessel Functions and Functions Associated with Them910
  • 8.6 Mathieu Functions950
  • 8.7-8.8 Associated Legendre Functions958
  • 8.9 Orthogonal Polynomials982
  • 9.1 Hypergeometric Functions1005
  • 9.2 Confluent Hypergeometric Functions1022
  • 9.3 Meijer's G-Function1032
  • 9.4 MacRobert's E-Function1035
  • 9.5 Riemann's Zeta Functions zeta(z,q) and zeta(z), and the Functions Phi(z,s,v) and xi(s)1036
  • 9.6 Bernoulli Numbers and Polynomials, Euler Numbers1040
  • 9.7 Constants1045
  • Chapter 10 Vector Field Theory1049
  • 10.1-10.8 Vectors, Vector Operators, and Integral Theorems1049
  • Chapter 11 Algebraic Inequalities1059
  • 11.1-11.3 General Algebraic Inequalities1059
  • Chapter 12 Integral Inequalities1063
  • 12.11 Mean Value Theorems1063
  • 12.21 Differentiation of Definite Integral Containing a Parameter1064
  • 12.31 Integral Inequalities1064
  • 12.41 Convexity and Jensen's Inequality1066
  • 12.51 Fourier Series and Related Inequalities1066
  • Chapter 13 Matrices and Related Results1069
  • 13.11-13.12 Special Matrices1069
  • 13.21 Quadratic Forms1071
  • 13.31 Differentiation of Matrices1073
  • 13.41 The Matrix Exponential1074
  • Chapter 14 Determinants1075
  • 14.11 Expansion of Second- and Third-Order Determinants1075
  • 14.12 Basic Properties1075
  • 14.13 Minors and Cofactors of a Determinant1075
  • 14.14 Principal Minors1076
  • 14.15* Laplace Expansion of a Determinant1076
  • 14.16 Jacobi's Theorem1076
  • 14.17 Hadamard's Theorem1077
  • 14.18 Hadamard's Inequality1077
  • 14.21 Cramer's Rule1077
  • 14.31 Some Special Determinants1078
  • Chapter 15 Norms1081
  • 15.1-15.9 Vector Norms1081
  • 15.11 General Properties1081
  • 15.21 Principal Vector Norms1081
  • 15.31 Matrix Norms1082
  • 15.41 Principal Natural Norms1082
  • 15.51 Spectral Radius of a Square Matrix1083
  • 15.61 Inequalities Involving Eigenvalues of Matrices1084
  • 15.71 Inequalities for the Characteristic Polynomial1084
  • 15.81-15.82 Named Theorems on Eigenvalues1087
  • 15.91 Variational Principles1091
  • Chapter 16 Ordinary Differential Equations1093
  • 16.1-16.9 Results Relating to the Solution of Ordinary Differential Equations1093
  • 16.11 First-Order Equations1093
  • 16.21 Fundamental Inequalities and Related Results1094
  • 16.31 First-Order Systems1094
  • 16.41 Some Special Types of Elementary Differential Equations1097
  • 16.51 Second-Order Equations1098
  • 16.61-16.62 Oscillation and Non-Oscillation Theorems for Second-Order Equations1100
  • 16.71 Two Related Comparison Theorems1103
  • 16.81-16.82 Non-Oscillatory Solutions1103
  • 16.91 Some Growth Estimates for Solutions of Second-Order Equations1104
  • 16.92 Boundedness Theorems1106
  • Chapter 17 Fourier, Laplace, and Mellin Transforms1107
  • 17.1-17.4 Integral Transforms1107
  • Chapter 18 The z-Transform1135
  • 18.1-18.3 Definition, Bilateral, and Unilateral z-Transforms1135
  • References1141
  • Supplemental references1145
  • Index of Functions and Constants1151
  • General Index of Concepts1161
Book details
  • Vendor Elsevier S & T
  • SKU 9780123736376
  • ISBN-13 9780080471112
  • Author Jeffrey, Alan; Zwillinger, Daniel
  • Edition 7th
  • Category Mathematics
  • Subject Reference

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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