Standard Mathematical Tables and Formulae - ICDST

31st

EDITION

CRC

standard MathematicAL TABLES and formulae

DANIEL ZWILLINGER

CHAPMAN & HALL/CRC

A CRC Press Company Boca Raton London New York Washington, D.C. ? 2003 by CRC Press LLC

Editor-in-Chief

Daniel Zwillinger Rensselaer Polytechnic Institute Troy, New York

Associate Editors

Steven G. Krantz Washington University St. Louis, Missouri

Kenneth H. Rosen AT&T Bell Laboratories Holmdel, New Jersey

Editorial Advisory Board

George E. Andrews Pennsylvania State University University Park, Pennsylvania

Michael F. Bridgland Center for Computing Sciences Bowie, Maryland

J. Douglas Faires Youngstown State University Youngstown, Ohio

Gerald B. Folland University of Washington Seattle, Washington

Ben Fusaro Florida State University Tallahassee, Florida

Alan F. Karr National Institute Statistical Sciences Research Triangle Park, North Carolina

Al Marden University of Minnesota Minneapolis, Minnesota

William H. Press Los Alamos National Lab Los Alamos, NM 87545

? 2003 by CRC Press LLC

Preface

It has long been the established policy of CRC Press to publish, in handbook form, the most up-to-date, authoritative, logically arranged, and readily usable reference material available. Prior to the preparation of this 31 st Edition of the CRC Standard Mathematical Tables and Formulae, the content of such a book was reconsidered. The previous edition was carefully analyzed, and input was obtained from practitioners in the many branches of mathematics, engineering, and the physical sciences. The consensus was that numerous small additions were required in several sections, and several new areas needed to be added.

Some of the new materials included in this edition are: game theory and voting power, heuristic search techniques, quadratic elds, reliability, risk analysis and decision rules, a table of solutions to Pell's equation, a table of irreducible polynomials

in ? ? , a longer table of prime numbers, an interpretation of powers of 10, a col-

lection of "proofs without words", and representations of groups of small order. In total, there are more than 30 completely new sections, more than 50 new and modi ed entries in the sections, more than 90 distinguished examples, and more than a dozen new tables and gures. This brings the total number of sections, sub-sections, and sub-sub-sections to more than 1,000. Within those sections are now more than 3,000 separate items (a de nition , a fact, a table, or a property). The index has also been extensively re-worked and expanded to make nding results faster and easier; there are now more than 6,500 index references (with 75 cross-references of terms) and more than 750 notation references.

The same successful format which has characterized earlier editions of the Handbook is retained, while its presentation has been updated and made more consistent from page to page. Material is presented in a multi-sectional format, with each section containing a valuable collection of fundamental reference material--tabular and expository.

In line with the established policy of CRC Press, the Handbook will be kept as current and timely as is possible. Revisions and anticipated uses of newer materials and tables will be introduced as the need arises. Suggestions for the inclusion of new material in subsequent editions and comments regarding the present edition are welcomed. The home page for this book, which will include errata, will be maintained at ht?tp?:?//w?w??w?.?ma?th?ta?ble?.com? /.? ??

The major material in this new edition is as follows:

Chapter 1: Analysis begins with numbers and then combines them into series and products. Series lead naturally into Fourier series. Numbers also lead to functions which results in coverage of real analysis, complex analysis, and generalized functions.

Chapter 2: Algebra covers the different types of algebra studied: elementary algebra, vector algebra, linear algebra, and abstract algebra. Also included are details on polynomials and a separate section on number theory. This chapter includes many new tables.

Chapter 3: Discrete Mathematics covers traditional discrete topics such as combinatorics, graph theory, coding theory and information theory, operations re-

? 2003 by CRC Press LLC

search, and game theory. Also included in this chapter are logic, set theory, and chaos. Chapter 4: Geometry covers all aspects of geometry: points, lines, planes, surfaces, polyhedra, coordinate systems, and differential geometry. Chapter 5: Continuous Mathematics covers calculus material: differentiation, integration, differential and integral equations, and tensor analysis. A large table of integrals is included. This chapter also includes differential forms and orthogonal coordinate systems. Chapter 6: Special Functions contains a sequence of functions starting with the trigonometric, exponential, and hyperbolic functions, and leading to many of the common functions encountered in applications: orthogonal polynomials, gamma and beta functions, hypergeometric functions, Bessel and elliptic functions, and several others. This chapter also contains sections on Fourier and Laplace transforms, and includes tables of these transforms. Chapter 7: Probability and Statistics begins with basic probability information (de n ing several common distributions) and leads to common statistical needs (point estimates, con d ence intervals, hypothesis testing, and ANOVA). Tables of the normal distribution, and other distributions, are included. Also included in this chapter are queuing theory, Markov chains, and random number generation. Chapter 8: Scientific Computing explores numerical solutions of linear and nonlinear algebraic systems, numerical algorithms for linear algebra, and how to numerically solve ordinary and partial differential equations. Chapter 9: Financial Analysis contains the formulae needed to determine the return on an investment and how to determine an annuity (i.e., the cost of a mortgage). Numerical tables covering common values are included. Chapter 10: Miscellaneous contains details on physical units (de nition s and conversions), formulae for date computations, lists of mathematical and electronic resources, and biographies of famous mathematicians. It has been exciting updating this edition and making it as useful as possible. But it would not have been possible without the loving support of my family, Janet Taylor and Kent Taylor Zwillinger.

Daniel Zwillinger ?? ?? ? ? ???? ? ?

15 October 2002

? 2003 by CRC Press LLC

Contributors

Karen Bolinger Clarion University Clarion, Pennsylvania

Patrick J. Driscoll U.S. Military Academy West Point, New York

M. Lawrence Glasser Clarkson University Potsdam, New York

Jeff Goldberg University of Arizona Tucson, Arizona

Rob Gross Boston College Chestnut Hill, Massachusetts

George W. Hart SUNY Stony Brook Stony Brook, New York

Melvin Hausner Courant Institute (NYU) New York, New York

Victor J. Katz MAA Washington, DC

Silvio Levy MSRI Berkeley, California

Michael Mascagni Florida State University Tallahassee, Florida

Ray McLenaghan University of Waterloo Waterloo, Ontario, Canada

John Michaels SUNY Brockport Brockport, New York

Roger B. Nelsen Lewis & Clark College Portland, Oregon

William C. Rinaman LeMoyne College Syracuse, New York

Catherine Roberts College of the Holy Cross Worcester, Massachusetts

Joseph J. Rushanan MITRE Corporation Bedford, Massachusetts

Les Servi MIT Lincoln Laboratory Lexington, Massachusetts

Peter Sherwood Interactive Technology, Inc. Newton, Massachusetts

Neil J. A. Sloane AT&T Bell Labs Murray Hill, New Jersey

Cole Smith University of Arizona Tucson, Arizona

Mike Sousa Veridian Ann Arbor, Michigan

Gary L. Stanek Youngstown State University Youngstown, Ohio

Michael T. Strauss HME Newburyport, Massachusetts

Nico M. Temme CWI Amsterdam, The Netherlands

Ahmed I. Zayed DePaul University Chicago, Illinois

? 2003 by CRC Press LLC

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