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Table of integrals, series, and products

Title: Table of integrals, series, and products / I.S. Gradshteyn and I.M. Ryzhik ; Alan Jeffrey, editor ; Daniel Zwillinger, associate editor ; translated from the Russian by Scripta Technica, Inc.
Author: Gradshteĭn, I. S. (Izrailʹ Solomonovich)
Publication: San Diego : Academic Press, ©2000.

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Request for On-site Use Request Scan How do I pick up this item and when will it be ready?	Text	Use in library	QA55 .G6613 2000	Off-site

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Description

xlvii, 1163 pages; 25 cm

Summary

The Table of Integrals, Series, and Products is the major reference source for integrals in the English language. It is essential for mathematicians, scientists, and engineers, who rely on it when identifying and subsequently solving extremely complex problems. The Sixth Edition is a corrected and expanded version of the previous edition. It was completely reset in order to add more material and to enhance the visual appearance of the information. 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. Preface 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 theses contributors is shown in the form of an acknowledgement list on page xxiii. This list gives the names of those who have written to us 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. Kölbig have contributed new.
Material, corrections, and suggestions for new material. Great care was taken to check the reset version of Gradshteyn and Ryzhik against the fifth edition, both by computer means and hand inspection, but it is inevitable that some transcription errors will remain. These will be rectified in subsequent reprinting of the book as and when they are identified. The authors would appreciate knowledge of any errors or deficiencies, their email addresses are listed below. If any errata are found, they will be posted on the website, www.az-tec.com/gr/errata. As in the previous edition, a numerical superscript added to an entry number is used to indicate either a new edition to the book or a correction. When an entire section is new, an asterisk has been added only to the section heading. Continuing in the previous convention, a superscript 10 has been added to entry numbers to indicate the most recent changes that have been made. This latest version of Gradshteyn and Ryzhik also forms the source for a revised.
Electronic version of Gradshteyn and Ryzhik. Special thanks are extended to John Law and the Newcastle University Computing Service for their help in the preparation of this edition. Alan Jeffrey Daniel Zwillinger.

Uniform Title

Tablit︠s︡y integralov, summ, ri︠a︡dov i proizvedeniĭ. English

Alternative Title

Tablit︠s︡y integralov, summ, ri︠a︡dov i proizvedeniĭ.

Subject

Genre/Form

Tables.
tables (documents)
Tables (Data)
Tables (Données)

Bibliography (note)

Includes bibliographical references (p. 1133-1142).

Contents

Finite sums -- Numerical series and infinite products -- Functional series -- Certain formulas from differential calculus -- Elementary Functions -- Power of Binomials -- The Exponential Function -- Trigonometric and Hyperbolic Functions -- The Logarithm -- The Inverse Trigonometric and Hyperbolic Functions -- Indefinite Integrals of Elementary Functions -- Rational functions -- Algebraic functions -- The Exponential Function -- Hyperbolic Functions -- Trigonometric Functions -- Logarithms and Inverse-Hyperbolic Functions -- Inverse Trigonometric Functions -- Definite Integrals of Elementary Functions -- Power and Algebraic Functions -- Exponential Functions -- Hyperbolic Functions -- Trigonometric Functions -- Logarithmic Functions -- Inverse Trigonometric Functions -- Multiple Integrals -- Indefinite Integrals of Special Functions -- Elliptic Integrals and Functions -- The Exponential Integral Function -- The Sine Integral and the Cosine Integral -- The Probability Integral and Fresnel Integrals -- Bessel Functions -- Definite Integrals of Special Functions -- Elliptic Integrals and Functions -- The Exponential Integral Function and Functions Generated by It -- The Gamma Function and Functions Generated by It -- Bessel Functions -- Functions Generated by Bessel Functions -- Mathieu Functions -- Associated Legendre Functions -- Orthogonal Polynomials -- Hypergeometric Functions -- Confluent Hypergeometric Functions -- Parabolic Cylinder Functions -- Meijer's and MacRobert's Functions (G and E) -- Special Functions -- Elliptic integrals and functions -- The Exponential Integral Function and Functions Generated by It -- Euler's Integrals of the First and Second Kinds -- Bessel Functions and Functions Associated with Them -- Mathieu Functions -- Associated Legendre Functions -- Orthogonal Polynomials -- Hypergeometric Functions -- Confluent Hypergeometric Functions -- Meijer's G-Function -- MacRobert's E-Function -- Riemann's Zeta Functions [zeta] (z, q), and [zeta] (z), and the Functions [Phi] (z, s, v) and [xi] (s) -- Bernoulli numbers and polynomials, Euler numbers -- Constants -- Vector Field Theory -- Vectors, Vector Operators, and Integral Theorems -- Algebraic Inequalities -- General Algebraic Inequalities -- Integral Inequalities -- Mean value theorems -- Differentiation of definite integral containing a parameter -- Integral inequalities -- Convexity and Jensen's inequality -- Fourier series and related inequalities -- Matrices and related results -- Special matrices -- Quadratic forms -- Differentiation of matrices -- The matrix exponential -- Determinants -- Expansion of second- and third-order determinants -- Basic properties -- Minors and cofactors of a determinant -- Principal minors -- Laplace expansion of a determinant -- Jacobi's theorem -- Hadamard's theorem -- Hadamard's inequality -- Cramer's rule -- Some special determinants -- Norms -- Vector Norms -- General properties -- Principal vector norms -- Matrix norms -- Principal natural norms -- Spectral radius of a square matrix -- Inequalities involving eigenvalues of matrices -- Inequalities for the characteristic polynomial -- Named theorems on eigenvalues -- Variational principles -- Ordinary differential equations -- Results relating to the solution of ordinary differential equations -- First-order equations -- Fundamental inequalities and related results -- First-order systems -- Some special types of elementary differential equations -- Second-order equations -- Oscillation and non-oscillation theorems for second-order equations -- Two related comparison theorems -- Non-oscillatory solutions -- Some growth estimates for solutions of second-order equations -- Boundedness theorems -- Fourier, Laplace, and Mellin Transforms -- Integral Transforms -- The z-transform -- Definition, Bilateral, and Unilateral z-Transforms.

ISBN

0122947576
9780122947575

LCCN

00104373

OCLC

ocm45091431
45091431
SCSB-1147892

Owning Institutions

Princeton University Library