Table of Integrals, Series, and Products
by Jeffrey; ZwillingerEdition: 6th
Format: Hardcover
Pub. Date: 2000-08-11
Publisher(s): Elsevier Science & Technology
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Summary
The Table of Integrals, Series, and Productslt;/b> is the major reference source for integrals in the English language. It is essential for mathematicians, scientists, and engineers, who rely on it when identifying and subsequently solving extremely complex problems. The Sixth Edition is a corrected and expanded version of the previous edition. It was completely reset in order to add more material and to enhance the visual appearance of the information. to preserve compatibility with the previous edition, the original numbering system for entries has been retained. New entries and sections have been inserted in a manner consistent with the original scheme. Whenever possible, new entries and corrections have been checked by means of symbolic computation. -Completely reset edition of Gradshteyn and Ryzhik reference book -New entries and sections kept in orginal numbering system with an expanded bibliography -Enlargement of material on orthogonal polynomials, theta functions, Laplace and Fourier transform pairs and much more.
Table of Contents
| Preface to the Sixth Edition | p. xxi |
| Acknowledgments | p. xxiii |
| The order of presentation of the formulas | p. xxvii |
| Use of the tables | p. xxxi |
| Special functions | p. xxxix |
| Notation | p. xliii |
| Note on the bibliographic references | p. xlvii |
| Introduction | p. 1 |
| Finite sums | p. 1 |
| Numerical series and infinite products | p. 6 |
| Functional series | p. 15 |
| Certain formulas from differential calculus | p. 21 |
| Elementary Functions | p. 25 |
| Power of Binomials | p. 25 |
| The Exponential Function | p. 26 |
| Trigonometric and Hyperbolic Functions | p. 27 |
| The Logarithm | p. 51 |
| The Inverse Trigonometric and Hyperbolic Functions | p. 54 |
| Indefinite Integrals of Elementary Functions | p. 61 |
| Introduction | p. 61 |
| Rational functions | p. 64 |
| Algebraic functions | p. 80 |
| The Exponential Function | p. 104 |
| Hyperbolic Functions | p. 105 |
| Trigonometric Functions | p. 147 |
| Logarithms and Inverse-Hyperbolic Functions | p. 233 |
| Inverse Trigonometric Functions | p. 237 |
| Definite Integrals of Elementary Functions | p. 243 |
| Introduction | p. 243 |
| Power and Algebraic Functions | p. 248 |
| Exponential Functions | p. 331 |
| Hyperbolic Functions | p. 365 |
| Trigonometric Functions | p. 384 |
| Logarithmic Functions | p. 522 |
| Inverse Trigonometric Functions | p. 596 |
| Multiple Integrals | p. 604 |
| Indefinite Integrals of Special Functions | p. 615 |
| Elliptic Integrals and Functions | p. 615 |
| The Exponential Integral Function | p. 622 |
| The Sine Integral and the Cosine Integral | p. 623 |
| The Probability Integral and Fresnel Integrals | p. 623 |
| Bessel Functions | p. 624 |
| Definite Integrals of Special Functions | p. 625 |
| Elliptic Integrals and Functions | p. 625 |
| The Exponential Integral Function and Functions Generated by It | p. 630 |
| The Gamma Function and Functions Generated by It | p. 644 |
| Bessel Functions | p. 652 |
| Functions Generated by Bessel Functions | p. 745 |
| Mathieu Functions | p. 755 |
| Associated Legendre Functions | p. 762 |
| Orthogonal Polynomials | p. 788 |
| Hypergeometric Functions | p. 806 |
| Confluent Hypergeometric Functions | p. 814 |
| Parabolic Cylinder Functions | p. 835 |
| Meijer's and MacRobert's Functions (G and E) | p. 843 |
| Special Functions | p. 851 |
| Elliptic integrals and functions | p. 851 |
| The Exponential Integral Function and Functions Generated by It | p. 875 |
| Euler's Integrals of the First and Second Kinds | p. 883 |
| Bessel Functions and Functions Associated with Them | p. 900 |
| Mathieu Functions | p. 940 |
| Associated Legendre Functions | p. 948 |
| Orthogonal Polynomials | p. 972 |
| Hypergeometric Functions | p. 995 |
| Confluent Hypergeometric Functions | p. 1012 |
| Meijer's G-Function | p. 1022 |
| MacRobert's E-Function | p. 1025 |
| Riemann's Zeta Functions [zeta] (z, q), and [zeta] (z), and the Functions [Phi] (z, s, v) and [xi] (s) | p. 1026 |
| Bernoulli numbers and polynomials, Euler numbers | p. 1030 |
| Constants | p. 1035 |
| Vector Field Theory | p. 1039 |
| Vectors, Vector Operators, and Integral Theorems | p. 1039 |
| Algebraic Inequalities | p. 1049 |
| General Algebraic Inequalities | p. 1049 |
| Integral Inequalities | p. 1053 |
| Mean value theorems | p. 1053 |
| Differentiation of definite integral containing a parameter | p. 1054 |
| Integral inequalities | p. 1054 |
| Convexity and Jensen's inequality | p. 1056 |
| Fourier series and related inequalities | p. 1056 |
| Matrices and related results | p. 1059 |
| Special matrices | p. 1059 |
| Quadratic forms | p. 1061 |
| Differentiation of matrices | p. 1063 |
| The matrix exponential | p. 1064 |
| Determinants | p. 1065 |
| Expansion of second- and third-order determinants | p. 1065 |
| Basic properties | p. 1065 |
| Minors and cofactors of a determinant | p. 1065 |
| Principal minors | p. 1066 |
| Laplace expansion of a determinant | p. 1066 |
| Jacobi's theorem | p. 1066 |
| Hadamard's theorem | p. 1066 |
| Hadamard's inequality | p. 1067 |
| Cramer's rule | p. 1067 |
| Some special determinants | p. 1068 |
| Norms | p. 1071 |
| Vector Norms | p. 1071 |
| General properties | p. 1071 |
| Principal vector norms | p. 1071 |
| Matrix norms | p. 1072 |
| Principal natural norms | p. 1072 |
| Spectral radius of a square matrix | p. 1073 |
| Inequalities involving eigenvalues of matrices | p. 1074 |
| Inequalities for the characteristic polynomial | p. 1074 |
| Named theorems on eigenvalues | p. 1076 |
| Variational principles | p. 1081 |
| Ordinary differential equations | p. 1083 |
| Results relating to the solution of ordinary differential equations | p. 1083 |
| First-order equations | p. 1083 |
| Fundamental inequalities and related results | p. 1084 |
| First-order systems | p. 1085 |
| Some special types of elementary differential equations | p. 1087 |
| Second-order equations | p. 1088 |
| Oscillation and non-oscillation theorems for second-order equations | p. 1090 |
| Two related comparison theorems | p. 1093 |
| Non-oscillatory solutions | p. 1093 |
| Some growth estimates for solutions of second-order equations | p. 1094 |
| Boundedness theorems | p. 1096 |
| Fourier, Laplace, and Mellin Transforms | p. 1099 |
| Integral Transforms | p. 1099 |
| The z-transform | p. 1127 |
| Definition, Bilateral, and Unilateral z-Transforms | p. 1127 |
| References | p. 1133 |
| Supplemental references | p. 1137 |
| Function and constant index | p. 1143 |
| General index | p. 1153 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
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