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Table of integrals, series, and products

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,...

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Bibliographic Details
Main Authors: Gradshteĭn, I. S., Ryzhik, I. M. (Author)
Other Authors: Zwillinger, Daniel (Editor), Moll, Victor H. (Editor)
Format: eBook
Language:English
Published: Waltham, MA Academic Press 2014
Edition:Eighth edition
Subjects:
Mathematics / Tables
Physical Sciences & Mathematics
Mathematics / General
Mathématiques / Tables
Mathematics / Fast
Mathematics
Online Access:
Collection: O'Reilly - Collection details see MPG.ReNa
Table of Contents:
  • Front Cover
  • Table of Integrals, Series, and Products
  • Copyright
  • Contents
  • 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
  • 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
  • 0.11 Progressions
  • 0.12 Sums of powers of natural numbers
  • 0.13 Sums of reciprocals of natural numbers
  • 0.14 Sums of products of reciprocals of natural numbers
  • 0.15 Sums of the binomial coefficients
  • 0.2 Numerical series and infinite products
  • 0.21 The convergence of numerical series
  • 0.22 Convergence tests
  • 0.23-0.24 Examples of numerical series
  • 0.25 Infinite products
  • 0.26 Examples of infinite products
  • 0.3 Functional series
  • 0.30 Definitions and theorems
  • 0.31 Power series
  • 0.32 Fourier series
  • 0.33 Asymptotic series
  • 0.4 Certain formulas from differential calculus
  • 0.41 Differentiation of a definite integral with respect to a parameter
  • 0.42 The nth derivative of a product (Leibniz's rule)
  • 0.43 The nth derivative of a composite function
  • 0.44 Integration by substitution
  • 1 Elementary Functions
  • 1.1 Power of Binomials
  • 1.11 Power series
  • 1.12 Series of rational fractions
  • 1.2 The Exponential Function
  • 1.21 Series representation
  • 1.22 Functional relations
  • 1.23 Series of exponentials
  • 1.3-1.4 Trigonometric and Hyperbolic Functions
  • 1.30 Introduction
  • 1.31 The basic functional relations
  • Includes bibliographical references and index
  • 3.46-3.48 Combinations of exponentials of more complicated arguments and powers
  • 3.5 Hyperbolic Functions
  • 3.51 Hyperbolic functions
  • 3.52-3.53 Combinations of hyperbolic functions and algebraic functions
  • 3.54 Combinations of hyperbolic functions and exponentials
  • 3.55-3.56 Combinations of hyperbolic functions, exponentials, and powers
  • 3.6-4.1 Trigonometric Functions
  • 3.61 Rational functions of sines and cosines and trigonometric functions of multiple angles
  • 3.62 Powers of trigonometric functions
  • 3.63 Powers of trigonometric functions and trigonometric functions of linear functions
  • 3.64-3.65 Powers and rational functions of trigonometric functions
  • 3.66 Forms containing powers of linear functions of trigonometric functions
  • 3.67 Square roots of expressions containing trigonometric functions
  • 3.68 Various forms of powers of trigonometric functions
  • 3.69-3.71 Trigonometric functions of more complicated arguments
  • 3.72-3.74 Combinations of trigonometric and rational functions
  • 3.75 Combinations of trigonometric and algebraic functions
  • 3.76-3.77 Combinations of trigonometric functions and powers
  • 3.78-3.81 Rational functions of x and of trigonometric functions
  • 3.82-3.83 Powers of trigonometric functions combined with other powers
  • 3.84 Integrals containing 1 − k2 sin2 x, 1 − k2 cos2 x, and similar expressions
  • 3.85-3.88 Trigonometric functions of more complicated arguments combined with powers
  • 3.89-3.91 Trigonometric functions and exponentials
  • 3.92 Trigonometric functions of more complicated arguments combined with exponentials
  • 3.93 Trigonometric and exponential functions of trigonometric functions
  • 3.94-3.97 Combinations involving trigonometric functions, exponentials, and powers
  • 3.98-3.99 Combinations of trigonometric and hyperbolic functions

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