Jerome Spanier – författare

koldham@trentu.ca,jmyland@trentu.caorjspanier@uci.edu.AnErrataofknownerrorsandrevisionswillbefound on the publisher's website; please access www.springer.com/978-0-387-48806-6 and follow the links. This will be updated as and if new errors are detected or clarifications are found to be needed. Use of the Atlas of Functions or Equator, the Atlas function calculator is at your own risk. The authors and the publisher disclaim liability for any direct or consequential damage resulting from use of the Atlas or Equator. It is a pleasure to express our gratitude to Michelle Johnston, Sten Engblom, and Trevor Mace-Brickman for theirhelpinthecreationoftheAtlasandEquator. Thefrankcommentsofseveralreviewerswhoinspectedanearly versionofthemanuscripthavealsobeenofgreatvalue. WegivesincerethankstoSpringer,andparticularlytoAnn KostantandOonaSchmid,fortheircommitmenttothelengthytaskofcarryingtheconceptofAnAtlasofFunctions through to reality with thoroughness, enthusiasm, skill, and even some humor. Their forbearance in dealing with the authors is particularly appreciated. WehopeyouwillenjoyusingAnAtlasofFunctionsandEquator,andthattheywillprovehelpfulinyourwork or studies. January 2008 Keith B.Oldham Jan C. Myland Jerome Spanier Every chapter has sections devoted to: notation, behavior, definitions, special cases, intrarelationships, expansions, particular values, numerical values, limits and approximations, operations of the calculus, complex argument, generalizations, and cognate functions. In addition, each chapter has the special features itemized below its title. PREFACE v GENERAL CONSIDERATIONS 1 What functions are. Organization of the Atlas. Notational conventions. Rules of the calculus. THE CONSTANT FUNCTION c 13 Mathematical constants. Complex numbers. Pulse functions. Series of powers of natural numbers. THE FACTORIAL FUNCTION n!21 Double and triple factorial functions. Combinatorics. Stirling numbers of the second kind. THE ZETA NUMBERS AND RELATED FUNCTIONS 29 Special values. Apery's constant. The Debye functions of classical physics.

This book comprehensively covers several hundred functions or function families. In chapters that progress by degree of complexity, it starts with simple, integer-valued functions then moves on to polynomials, Bessel, hypergeometric and hundreds more.

This book represents the refereed proceedings of the Third International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at Claremont Graduate University in 1998. An important feature are invited surveys of the state of the art in key areas such as multidimensional numerical integration, low-discrepancy point sets, random number generation, and applications of Monte Carlo and quasi-Monte Carlo methods. These proceedings include also carefully selected contributed papers on all aspects of Monte Carlo and quasi-Monte Carlo methods. The reader will be informed about current research in this very active area.