Book description
The eighth edition of the classic Gradshteyn and Ryzhik is an updated completely revised edition of what is acknowledged universally by mathematical and applied science users as the key reference work concerning the integrals and special functions. The book is valued by users of previous editions of the work both for its comprehensive coverage of integrals and special functions, and also for its accuracy and valuable updates. Since the first edition, published in 1965, the mathematical content of this book has significantly increased due to the addition of new material, though the size of the book has remained almost unchanged. The new 8th edition contains entirely new results and amendments to the auxiliary conditions that accompany integrals and wherever possible most entries contain valuable references to their source.
 Over 10, 000 mathematical entries
 Most up to date listing of integrals, series and products (special functions)
 Provides accuracy and efficiency in industry work
 25% of new material not including changes to the restrictions on results that revise the range of validity of results, which lend to approximately 35% of new updates
Table of contents
 Cover image
 Title page
 Table of Contents
 Copyright
 Preface to the Eighth Edition
 Acknowledgments
 The Order of Presentation of the Formulas

Use of the Tables*
 Bernoulli and Euler Polynomials and Numbers
 Elliptic Functions and Elliptic Integrals
 The Jacobi Zeta Function and Theta Functions
 The Factorial (Gamma) Function
 Exponential and Related Integrals
 Hermite and Chebyshev Orthogonal Polynomials
 Bessel Functions
 Parabolic Cylinder Functions and Whittaker Functions
 Mathieu Functions
 Index of Special Functions
 Notation
 Note on the Bibliographic References
 0. Introduction
 1. Elementary Functions
 2. Indefinite Integrals of Elementary Functions
 34. Definite Integrals of Elementary Functions

4. Definite Integrals of Elementary Functions
 4.11–4.12 Combinations involving trigonometric and hyperbolic functions and powers
 4.13 Combinations of trigonometric and hyperbolic functions and exponentials
 4.14 Combinations of trigonometric and hyperbolic functions, exponentials, and powers
 4.2–4.4 Logarithmic Functions
 4.5 Inverse Trigonometric Functions
 4.6 Multiple Integrals

5. Indefinite Integrals of Special Functions
 5.1 Elliptic Integrals and Functions
 5.13 Jacobian elliptic functions
 5.14 Weierstrass elliptic 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 Functions
 5.6 Orthogonal Polynomials
 5.7 Hypergeometric Functions

67. Definite Integrals of Special Functions
 6.1 Elliptic Integrals and Functions
 6.2–6.3 The Exponential Integral Function and Functions Generated by It
 6.22–6.23 The exponential integral function
 6.24–6.26 The sine integral and cosine integral functions
 6.27 The hyperbolic sine integral and hyperbolic cosine integral functions
 6.28–6.31 The probability integral
 6.32 Fresnel integrals
 6.4 The Gamma Function and Functions Generated by It
 6.466.47 The Function ψ(x)
 6.56.7 Bessel Functions
 6.8 Functions Generated by Bessel Functions
 6.9 Mathieu Functions

7. Definite Integrals of Special Functions
 7.17.2 Associated Legendre Functions
 7.3–7.4 Orthogonal Polynomials
 7.325* Complete System of Orthogonal Step Functions
 7.33 Combinations of the polynomials Cnv(x) and Bessel functions. Integration of Gegenbauer functions with respect to the index
 7.34 Combinations of Chebyshev polynomials and powers
 7.35 Combinations of Chebyshev polynomials and elementary functions
 7.36 Combinations of Chebyshev polynomials and Bessel functions
 7.37−7.38 Hermite polynomials
 7.39 Jacobi polynomials
 7.41–7.42 Laguerre polynomials
 7.5 Hypergeometric Functions
 7.53 Hypergeometric and trigonometric functions
 7.54 Combinations of hypergeometric and Bessel functions
 7.6 Confluent Hypergeometric Functions
 7.68 Combinations of confluent hypergeometric functions and other special functions
 7.69 Integration of confluent hypergeometric functions with respect to the index
 7.7 Parabolic Cylinder Functions
 7.8 Meijer's and MacRobert's Functions (G and E)
 8. Special Functions

9. Special Functions
 9.1 Hypergeometric Functions
 9.2 Confluent Hypergeometric Functions
 9.3 Meijer's GFunction
 9.4 MacRobert's EFunction
 9.5 Riemann's Zeta Functions ζ(z, q), and ζ(z), and the Functions Φ(z, s, v) and ξ(s)
 9.6 Bernoulli Numbers and Polynomials, Euler Numbers, the Functions v(x), v(x, α), μ(x, β), μ(x, β, α), λ(, α), μ(x, β), μ(x, β, α), λ(x, y) and Euler Polynomials
 9.7 Constants
 10. Vector Field Theory
 11. Integral Inequalities
 12. Fourier, Laplace, and Mellin Transforms
 Bibliographic References
 Supplementary References
 Index of Functions and Constants
 Index of Concepts
Product information
 Title: Table of Integrals, Series, and Products, 8th Edition
 Author(s):
 Release date: September 2014
 Publisher(s): Academic Press
 ISBN: 9780123849342
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