This completely reset sixth edition of Gradshteyn and Ryzhik is a corrected and expanded version of the previous edition. The book was completely reset in order to add more material and to enhance the visual appearance of the material. 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. The diverse ways in which corrections have been contributed have made it impossible to attribute them to reference sources that are accessible to users of this book. However, as in previous editions, our indebtedness to these contributors is shown in the form of an acknowledgment list on page xxiii. This list gives the names of those who have written to ns directly' sending corrections and suggestions for addenda, and added to it are the names of those who have published errata in Mathematics of Computation. Certain individuals must be singled out for special thanks due to their significant contributions: Professors H. van Haeringen and L; P. Kok of The Netherlands and Dr. K. S. Ko1big have contributed new material, corrections, and suggestions for new material.
Preface to the Sixth Edition Acknowledgments The order of presentation of the formulas Use of the tables Special functions Notation Note on the bibliographic references 0 Introduction 0.1 Finite sums 0.2 Numerical series and infinite products 0.3 Functional series 0.4 Certain formulas from differential calculus1 Elementary Functions 1.1 Power of Binomials 1.2 The Exponential Function 1.3-1.4 Trigonometric and Hyperbolic Functions 1.5 The Logarithm 1.6 The Inverse Trigonometric and Hyperbolic Functions 2 Indefinite Integrals of Elementary Functions 2.0 Introduction 2.1 Rational functions 2.2 Algebraic functions 2.3 Te Exponential Function 2.4 Hyperbolic Functions 2.5-2.6 Trigonometric Functions 2.7 Logarithms and Inverse-Hyperbolic Functions 2.8 Inverse Trigonometric Functions3-4 Definite Integrals of Elementary Functions 3.0 Introduction 3.1-3.2 Power and Algebraic Functions 3.3-3.4 Exponential Functions 3.5 Hyperbolic Functions 3.6-4.1 Trigonometric Functions 4.2-4.4 Logarithmic Functions 4.5 Inverse Trigonometric Functions 4.6 Multiple Integrals5 Indefinite Integrals of Special Functions 5.1 Elliptic Integrals and Functions 5.2 The Exponential Integral Function 5.3 The Sine Integral and the Cosine Integral 5.4 The Probability Integral and Fresnel Integrals 5.5 Bessel Functions6-7 Definite Integrals of Special Functions……8-9 Special Functions10 Vector Field Theory11 Algebraic Inequalities12 Integral Inequalities13 Matrices and Related Results14 Determinants15 Norms16 Ordinary differential equations17 Fourier, Laplace, and Mellin Transforms18 The z-transformReferencesSupplemental referencesFunction and constant indexGeneral index
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