Table of Integrals, Series, and Products
1st Edition
Published on 10. May 2014
1206 pages
978-1-4832-6564-3 (ISBN)
Description
Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.
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Other editions
New editions
Daniel Zwillinger | Alan Jeffrey
Table of Integrals, Series, and Products
E-Book
08/2000
6th Edition
Academic Press
€91.95
Available for download
Additional editions
I.S. Gradshteyn | I.M. Ryzhik
Table of Integrals, Series and Products
Book
05/1980
2nd Edition
Academic Press
€42.09
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Content
¿Preface to the Corrected and Enlarged EditionPreface to the First EditionPreface to the Third EditionPreface to the Fourth EditionEditor's ForewordAcknowledgmentThe Order of Presentation of the FormulasUse of the TablesIndex of Special Functions and NotationsNotationsNote on the Bibliographic References0. 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 0.43 The nth Derivative of a Composite Function 0.44 Integration by Substitution1. 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 Representations 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 1.32 The Representation of Powers of Trigonometric and Hyperbolic Functions in Terms of Functions of Multiples of the Argument (Angle) 1.33 The Representation of Trigonometric and Hyperbolic Functions of Multiples of the Argument (angle) in Terms of Powers of these Functions 1.34 Certain Sums of Trigonometric and Hyperbolic Functions 1.35 Sums of Powers of Trigonometric Functions of Multiple Angles 1.36 Sums of Products of Trigonometric Functions of Multiple Angles 1.37 Sums of Tangents of Multiple Angles 1.38 Sums Leading To Hyperbolic Tangents and Cotangents 1.39 The Representation of Cosines and Sines of Multiples of the Angle as Finite Products 1.41 The Expansion of Trigonometric and Hyperbolic Functions in Power Series 1.42 Expansion in Series of Simple Fractions 1.43 Representation in the Form of an Infinite Product 1.44-1.45 Trigonometric (Fourier) Series 1.46 Series of Products of Exponential and Trigonometric Functions 1.47 Series of Hyperbolic Functions 1.48 Lobachevskiy's "Angle of Parallelism" ¿ (x) 1.49 The Hyperbolic Amplitude (The Gudermannian) gd x 1.5 The Logarithm 1.51 Series Representation 1.52 Series of Logarithms 1.6 The Inverse Trigonometric and Hyperbolic Functions 1.61 The Domain of Definition 1.62-1.63 Functional Relations2. Indefinite Integals of Elementary Functions 2.0 Introduction 2.00 General Remarks 2.01 The Basic Integrals 2.02 General Formulas 2.1 Rational Functions 2.10 General Integration Rules 2.11-2.13 Forms Containing the Binomial a + bxk 2.14 Forms Containing the Binomial 1 ± xn 2.15 Forms Containing Pairs of Binomials: a + bx and a + ßx 2.16 Forms Containing the Trinomial a + bxk + cx2k 2.17 Forms Containing the Quadratic Trinomial a + bx + Cx2 and Powers of x 2.18 Forms Containing the Quadratic Trinomial a + bx + Cx2 and the Binomial a + ßx 2.2 Algebraic Functions 2.20 Introduction 2.21 Forms Containing the Binomial a + bxk and vx 2.22-2.23 Forms Containing xv(a + bx)k 2.24 Forms Containing va + bx and he Binomial a + ßx 2.
