Table of Integrals, Series, and Products - Edition 8 - Edited by Daniel Zwillinger Elsevier Inspection Copies

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Table of Integrals, Series, and Products,

Edition 8

Edited by Daniel Zwillinger

Publication Date: 18 Sep 2014

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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 8^th 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.

Key Features

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

About the author

Edited by Daniel Zwillinger, Rensselaer Polytechnic Institute, Troy, NY, USA

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
- 0.1 Finite sums
- 0.2 Numerical series and infinite products
- 0.3 Functional series
- 0.4 Certain formulas from differential calculus
1. 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 The Exponential Function
- 2.4 Hyperbolic Functions
- 2.5–2.6 Trigonometric Functions
- 2.7 Logarithms and Inverse-Hyperbolic Functions
- 2.8 Inverse Trigonometric Functions
3-4. 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. 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
6-7. 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
- 6.46-6.47 The Function ?(x)
- 6.5-6.7 Bessel Functions
- 6.8 Functions Generated by Bessel Functions
- 6.9 Mathieu Functions
7. Definite Integrals of Special Functions
- 7.1-7.2 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

8. Special Functions

8.1 Elliptic Integrals and Functions

8.2 The Exponential Integral Function and Functions Generated by It

8.3 Euler's Integrals of the First and Second Kinds and Functions Generated by Them

8.4–8.5 Bessel Functions and Functions Associated with Them

9. Special Functions
- 9.5 Riemann's Zeta Functions ?(z, q), and ?(z), and the Functions F(z, s, v) and ?(s)
- 9.6 Bernoulli Numbers and Polynomials, Euler Numbers, the Functions v(x), v(x, a), µ(x, ß), µ(x, ß, a), ?(x, y) and Euler Polynomials
- 9.7 Constants
10. Vector Field Theory
- 10.1–10.8 Vectors, Vector Operators, and Integral Theorems
11. Integral Inequalities
- 11.11 Mean Value Theorems
- 11.21 Differentiation of Definite Integral Containing a Parameter
- 11.31 Integral Inequalities
- 11.41 Convexity and Jensen's Inequality
- 11.51 Fourier Series and Related Inequalities
12. Fourier, Laplace, and Mellin Transforms
- 12.1–12.4 Integral Transforms
Bibliographic References
Supplementary References
Index of Functions and Constants
Index of Concepts

ISBN: 9780123849335

Page Count: 1200

Retail Price : £78.99

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