Table of Integrals, Series, and Products / Edition 6

Table of Integrals, Series, and Products / Edition 6

by Alan Jeffrey
     
 

ISBN-10: 0122947576

ISBN-13: 9780122947575

Pub. Date: 08/28/2000

Publisher: Elsevier Science & Technology Books

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,

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Overview

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

Product Details

ISBN-13:
9780122947575
Publisher:
Elsevier Science & Technology Books
Publication date:
08/28/2000
Edition description:
Older Edition
Pages:
1163
Product dimensions:
7.92(w) x 9.62(h) x 2.32(d)

Table of Contents

Preface to the Sixth Editionxxi
Acknowledgmentsxxiii
The order of presentation of the formulasxxvii
Use of the tablesxxxi
Special functionsxxxix
Notationxliii
Note on the bibliographic referencesxlvii
0Introduction1
0.1Finite sums1
0.2Numerical series and infinite products6
0.3Functional series15
0.4Certain formulas from differential calculus21
1Elementary Functions25
1.1Power of Binomials25
1.2The Exponential Function26
1.3-1.4Trigonometric and Hyperbolic Functions27
1.5The Logarithm51
1.6The Inverse Trigonometric and Hyperbolic Functions54
2Indefinite Integrals of Elementary Functions61
2.0Introduction61
2.1Rational functions64
2.2Algebraic functions80
2.3The Exponential Function104
2.4Hyperbolic Functions105
2.5-2.6Trigonometric Functions147
2.7Logarithms and Inverse-Hyperbolic Functions233
2.8Inverse Trigonometric Functions237
3-4Definite Integrals of Elementary Functions243
3.0Introduction243
3.1-3.2Power and Algebraic Functions248
3.3-3.4Exponential Functions331
3.5Hyperbolic Functions365
3.6-4.1Trigonometric Functions384
4.2-4.4Logarithmic Functions522
4.5Inverse Trigonometric Functions596
4.6Multiple Integrals604
5Indefinite Integrals of Special Functions615
5.1Elliptic Integrals and Functions615
5.2The Exponential Integral Function622
5.3The Sine Integral and the Cosine Integral623
5.4The Probability Integral and Fresnel Integrals623
5.5Bessel Functions624
6-7Definite Integrals of Special Functions625
6.1Elliptic Integrals and Functions625
6.2-6.3The Exponential Integral Function and Functions Generated by It630
6.4The Gamma Function and Functions Generated by It644
6.5-6.7Bessel Functions652
6.8Functions Generated by Bessel Functions745
6.9Mathieu Functions755
7.1-7.2Associated Legendre Functions762
7.3-7.4Orthogonal Polynomials788
7.5Hypergeometric Functions806
7.6Confluent Hypergeometric Functions814
7.7Parabolic Cylinder Functions835
7.8Meijer's and MacRobert's Functions (G and E)843
8-9Special Functions851
8.1Elliptic integrals and functions851
8.2The Exponential Integral Function and Functions Generated by It875
8.3Euler's Integrals of the First and Second Kinds883
8.4-8.5Bessel Functions and Functions Associated with Them900
8.6Mathieu Functions940
8.7-8.8Associated Legendre Functions948
8.9Orthogonal Polynomials972
9.1Hypergeometric Functions995
9.2Confluent Hypergeometric Functions1012
9.3Meijer's G-Function1022
9.4MacRobert's E-Function1025
9.5Riemann's Zeta Functions [zeta] (z, q), and [zeta] (z), and the Functions [Phi] (z, s, v) and [xi] (s)1026
9.6Bernoulli numbers and polynomials, Euler numbers1030
9.7Constants1035
10Vector Field Theory1039
10.1-10.8Vectors, Vector Operators, and Integral Theorems1039
11Algebraic Inequalities1049
11.1-11.3General Algebraic Inequalities1049
12Integral Inequalities1053
12.11Mean value theorems1053
12.21Differentiation of definite integral containing a parameter1054
12.31Integral inequalities1054
12.41Convexity and Jensen's inequality1056
12.51Fourier series and related inequalities1056
13Matrices and related results1059
13.11-13.12Special matrices1059
13.21Quadratic forms1061
13.31Differentiation of matrices1063
13.41The matrix exponential1064
14Determinants1065
14.11Expansion of second- and third-order determinants1065
14.12Basic properties1065
14.13Minors and cofactors of a determinant1065
14.14Principal minors1066
14.15Laplace expansion of a determinant1066
14.16Jacobi's theorem1066
14.17Hadamard's theorem1066
14.18Hadamard's inequality1067
14.21Cramer's rule1067
14.31Some special determinants1068
15Norms1071
15.1-15.9Vector Norms1071
15.11General properties1071
15.21Principal vector norms1071
15.31Matrix norms1072
15.41Principal natural norms1072
15.51Spectral radius of a square matrix1073
15.61Inequalities involving eigenvalues of matrices1074
15.71Inequalities for the characteristic polynomial1074
15.81-15.82Named theorems on eigenvalues1076
15.91Variational principles1081
16Ordinary differential equations1083
16.1-16.9Results relating to the solution of ordinary differential equations1083
16.11First-order equations1083
16.21Fundamental inequalities and related results1084
16.31First-order systems1085
16.41Some special types of elementary differential equations1087
16.51Second-order equations1088
16.61-16.62Oscillation and non-oscillation theorems for second-order equations1090
16.71Two related comparison theorems1093
16.81-16.82Non-oscillatory solutions1093
16.91Some growth estimates for solutions of second-order equations1094
16.92Boundedness theorems1096
17Fourier, Laplace, and Mellin Transforms1099
17.1-17.4Integral Transforms1099
18The z-transform1127
18.1-18.3Definition, Bilateral, and Unilateral z-Transforms1127
References1133
Supplemental references1137
Function and constant index1143
General index1153

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