Table of Integrals, Series, and Products

Author: I. S. Gradshteyn,I. M. Ryzhik

Publisher: Academic Press

ISBN: 1483265641

Category: Mathematics

Page: 1206

View: 3500

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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Table of Integrals, Series, and Products

Author: Alan Jeffrey,Daniel Zwillinger

Publisher: Elsevier

ISBN: 9780080471112

Category: Mathematics

Page: 1200

View: 4156

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, it has been thoroughly revised and enlarged on a regular basis, with substantial additions and, where necessary, existing entries corrected or revised. The seventh edition includes a fully searchable CD-Rom. - Fully searchable CD that puts information at your fingertips included with text - Most up to date listing of integrals, series and products - Provides accuracy and efficiency in work
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Table of Integrals, Series, and Products

Author: Daniel Zwillinger

Publisher: Elsevier

ISBN: 0123849349

Category: Mathematics

Page: 1184

View: 3545

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
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Special Integrals of Gradshteyn and Ryzhik

the Proofs -

Author: Victor H. Moll

Publisher: CRC Press

ISBN: 1482256541

Category: Mathematics

Page: 263

View: 4501

A Guide to the Evaluation of Integrals Special Integrals of Gradshetyn and Ryzhik: the Proofs provides self-contained proofs of a variety of entries in the frequently used table of integrals by I.S. Gradshteyn and I.M. Ryzhik. The book gives the most elementary arguments possible and uses Mathematica® to verify the formulas. You will discover the beauty, patterns, and unexpected connections behind the formulas. Volume II collects 14 papers from Revista Scientia covering elliptic integrals, the Riemann zeta function, the error function, hypergeometric and hyperbolic functions, Bessel-K functions, logarithms and rational functions, polylogarithm functions, the exponential integral, and Whittaker functions. Many entries have a variety of proofs that can be evaluated using a symbolic language or point to the development of a new algorithm.
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Handbook of Special Functions

Derivatives, Integrals, Series and Other Formulas

Author: Yury A. Brychkov

Publisher: CRC Press

ISBN: 1584889578

Category: Mathematics

Page: 704

View: 6722

Because of the numerous applications involved in this field, the theory of special functions is under permanent development, especially regarding the requirements for modern computer algebra methods. The Handbook of Special Functions provides in-depth coverage of special functions, which are used to help solve many of the most difficult problems in physics, engineering, and mathematics. The book presents new results along with well-known formulas used in many of the most important mathematical methods in order to solve a wide variety of problems. It also discusses formulas of connection and conversion for elementary and special functions, such as hypergeometric and Meijer G functions.
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Zeta and Q-Zeta Functions and Associated Series and Integrals

Author: H. M. Srivastava,Choi Junesang

Publisher: Elsevier

ISBN: 0123852188

Category: Mathematics

Page: 657

View: 8885

Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory and applications of the basic (or q-) extensions of various special functions is included. This book will be invaluable because it covers not only detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions, but stimulating historical accounts of a large number of problems and well-classified tables of series and integrals. Detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions
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A guide to mathematical tables

Author: Aleksandr Vasilʹevich Lebedev,Rimma Maksimova Fedorova,Nina Mikhollovna Burunova

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 586

View: 1488

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Handbook of Differential Equations

Author: Daniel Zwillinger

Publisher: Academic Press

ISBN: 1483220966

Category: Mathematics

Page: 694

View: 9480

Handbook of Differential Equations is a handy reference to many popular techniques for solving and approximating differential equations, including exact analytical methods, approximate analytical methods, and numerical methods. Topics covered range from transformations and constant coefficient linear equations to finite and infinite intervals, along with conformal mappings and the perturbation method. Comprised of 180 chapters, this book begins with an introduction to transformations as well as general ideas about differential equations and how they are solved, together with the techniques needed to determine if a partial differential equation is well-posed or what the "natural" boundary conditions are. Subsequent sections focus on exact and approximate analytical solution techniques for differential equations, along with numerical methods for ordinary and partial differential equations. This monograph is intended for students taking courses in differential equations at either the undergraduate or graduate level, and should also be useful for practicing engineers or scientists who solve differential equations on an occasional basis.
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CRC Standard Mathematical Tables and Formulae

Author: Daniel Zwillinger

Publisher: CRC Press

ISBN: 1420035347

Category: Mathematics

Page: 928

View: 2953

A perennial bestseller, the 30th edition of CRC Standard Mathematical Tables and Formulae was the first "modern" edition of the handbook - adapted to be useful in the era of personal computers and powerful handheld devices. Now this version will quickly establish itself as the "user-friendly" edition. With a detailed table of contents and an extensive index listing over 6,000 entries, the 31st edition of this hugely successful handbook makes information even easier to locate. New in the 31st edition: Game theory and voting power Heuristic search techniques Quadratic fields Reliability Risk analysis and decision rules A table of solutions to Pell's equation A table of irreducible polynomials in Z2[x] An interpretation of powers of 10 A collection of "proofs without words" Representations of groups of small order Counting principles Tesselations and tilings ...and much more! An indispensable, up-to-date resource, CRC Standard Mathematical Tables and Formulae, 31st Edition makes it effortless to find the equations, tables, and formulae you need most often.
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Pocket Book of Integrals and Mathematical Formulas, 4th Edition

Author: Ronald J. Tallarida

Publisher: CRC Press

ISBN: 9781420063073

Category: Mathematics

Page: 286

View: 7303

Convenient Organization of Essential Material so You Can Look up Formulas Fast Containing a careful selection of standard and timely topics, the Pocket Book of Integrals and Mathematical Formulas, Fourth Edition presents many numerical and statistical tables, scores of worked examples, and the most useful mathematical formulas for engineering and scientific applications. This fourth edition of a bestseller provides even more comprehensive coverage with the inclusion of several additional topics, all while maintaining its accessible, clear style and handy size. New to the Fourth Edition • An expanded chapter on series that covers many fascinating properties of the natural numbers that follow from number theory • New applications such as geostationary satellite orbits and drug kinetics • An expanded statistics section that discusses nonlinear regression as well as the normal approximation of the binomial distribution • Revised format of the table of integrals for easier use of the forms and functions Easy to Use on the Go The book addresses a range of areas, from elementary algebra, geometry, matrices, and trigonometry to calculus, vector analysis, differential equations, and statistics. Featuring a convenient, portable size, it is sure to remain in the pockets or on the desks of all who use mathematical formulas and tables of integrals and derivatives.
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Handbook of Mathematical Functions

with Formulas, Graphs, and Mathematical Tables

Author: Milton Abramowitz,Irene A. Stegun

Publisher: Courier Corporation

ISBN: 0486158241

Category: Mathematics

Page: 1046

View: 7188

A classic resource for working with special functions, standard trig, and exponential logarithmic definitions and extensions, it features 29 sets of tables, some to as high as 20 places.
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Handbook of Mathematical Formulas

Author: Hans-Jochen Bartsch

Publisher: Academic Press

ISBN: 1483267423

Category: Mathematics

Page: 528

View: 694

Handbook of Mathematical Formulas presents a compilation of formulas to provide the necessary educational aid. This book covers the whole field from the basic rules of arithmetic, via analytic geometry and infinitesimal calculus through to Fourier's series and the basics of probability calculus. Organized into 12 chapters, this book begins with an overview of the fundamental notions of set theory. This text then explains linear expression wherein the variables are only multiplied by constants and added to constants or expressions of the same kind. Other chapters consider a variety of topics, including matrices, statistics, linear optimization, Boolean algebra, and Laplace's transforms. This book discusses as well the various systems of coordinates in analytical geometry. The final chapter deals with algebra of logic and its development into a two-value Boolean algebra as switching algebra. This book is intended to be suitable for students of technical schools, colleges, and universities.
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Asymptotic Approximations of Integrals

Computer Science and Scientific Computing

Author: R. Wong

Publisher: Academic Press

ISBN: 1483220710

Category: Mathematics

Page: 556

View: 5077

Asymptotic Approximations of Integrals deals with the methods used in the asymptotic approximation of integrals. Topics covered range from logarithmic singularities and the summability method to the distributional approach and the Mellin transform technique for multiple integrals. Uniform asymptotic expansions via a rational transformation are also discussed, along with double integrals with a curve of stationary points. For completeness, classical methods are examined as well. Comprised of nine chapters, this volume begins with an introduction to the fundamental concepts of asymptotics, followed by a discussion on classical techniques used in the asymptotic evaluation of integrals, including Laplace's method, Mellin transform techniques, and the summability method. Subsequent chapters focus on the elementary theory of distributions; the distributional approach; uniform asymptotic expansions; and integrals which depend on auxiliary parameters in addition to the asymptotic variable. The book concludes by considering double integrals and higher-dimensional integrals. This monograph is intended for graduate students and research workers in mathematics, physics, and engineering.
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Mathematical Handbook of Formulas and Tables

Author: Murray R. Spiegel,John Liu

Publisher: McGraw Hill Professional

ISBN: 9780070382039

Category: Mathematics

Page: 278

View: 9234

A study aid and reference offers more than 2400 formulas and tables covering elementary to advanced math.
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Special Functions and Orthogonal Polynomials

Author: Richard Beals,Roderick Wong

Publisher: Cambridge University Press

ISBN: 1107106982

Category: Mathematics

Page: 500

View: 4993

A comprehensive graduate-level introduction to classical and contemporary aspects of special functions.
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NIST Handbook of Mathematical Functions

Author: Frank W. J. Olver

Publisher: Cambridge University Press

ISBN: 0521192250

Category: Mathematics

Page: 951

View: 6897

The new standard reference on mathematical functions, replacing the classic but outdated handbook from Abramowitz and Stegun. Includes PDF version.
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Computing Highly Oscillatory Integrals

Author: Alfredo Deaño,Daan Huybrechs,Arieh Iserles

Publisher: SIAM

ISBN: 1611975123

Category: Mathematics

Page: 180

View: 1722

Highly oscillatory phenomena range across numerous areas in science and engineering and their computation represents a difficult challenge. A case in point is integrals of rapidly oscillating functions in one or more variables. The quadrature of such integrals has been historically considered very demanding. Research in the past 15 years (in which the authors played a major role) resulted in a range of very effective and affordable algorithms for highly oscillatory quadrature. This is the only monograph bringing together the new body of ideas in this area in its entirety. The starting point is that approximations need to be analyzed using asymptotic methods rather than by more standard polynomial expansions. As often happens in computational mathematics, once a phenomenon is understood from a mathematical standpoint, effective algorithms follow. As reviewed in this monograph, we now have at our disposal a number of very effective quadrature methods for highly oscillatory integrals--Filon-type and Levin-type methods, methods based on steepest descent, and complex-valued Gaussian quadrature. Their understanding calls for a fairly varied mathematical toolbox--from classical numerical analysis, approximation theory, and theory of orthogonal polynomials all the way to asymptotic analysis--yet this understanding is the cornerstone of efficient algorithms.
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