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.
Rezensionen / Stimmen
From the reviews of the second edition:
"The book is devoted to functions such as quadratic and cubic polynomials, absolute value, square roots, etc. . the Atlas comes with software for computing the functions described in the book. . the Atlas is valuable as a reference, it also contains a large amount of expository text. . The Atlas seems to have been written for the reader who is not in such a hurry and who might enjoy looking around a bit." (John Cook, The Mathematical Association of America, March, 2009)
"This is a compilation of several hundred functions that are frequently used by engineers, scientists, and mathematicians to obtain a quantitative result. . Each chapter in this handbook discusses a function or a family of related functions for a total of 65 chapters. . Each chapter contains definitions and properties for each function along with color graphs . . Engineers, scientists, and mathematicians will find this reference book to be a handy resource for manyyears." (Electrical Insulation Magazine, 2009)
"This book provides elementary and basic information on several hundred functions . . a combination of a book and software is useful for scientists concerned with the quantitative aspects of their field. . layout of the book is modern with very nice colorful graphs or surfaces of functions. Each chapter contains a lot of information about the functions studied in that chapter. . This book defends well its place in the mathematical literature." (Matti Vuorinen, Zentralblatt MATH, Vol. 1167, 2009)
"This is the second edition of a handbook with same title . . There are numerous other improvements throughout this new edition but the objective remains the same to provide the reader regardless of his or her discipline with a succinct compendium of information about all the common mathematical functions in use today. . The layout of the book is excellent and it is a pleasure to see the glossy paper and the very high quality graphs. The inclusion of Equator is a useful contribution." (Mourad E. H. Ismail, Mathematical Reviews, Issue 2010 f)
Auflage
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Research
Editions-Typ
Illustrationen
Maße
Höhe: 285 mm
Breite: 215 mm
Dicke: 44 mm
Gewicht
ISBN-13
978-0-387-48806-6 (9780387488066)
DOI
10.1007/978-0-387-48807-3
Schweitzer Klassifikation
Keith B. Oldham is a professor of Chemistry at Trent University in Ontario, Canada. He has co-authored several books, contributed to numerous others, and has published over 200 articles. He co-authored, with Jerome Spanier, the first edition of An Atlas of Functions.
Jan C. Myland is a Research Associate in Electrochemistry at Trent University.
Jerome Spanier is a prominent mathematics professor emeritus, currently a researcher at University of California, Irvine. He has received many prestigious honors and awards and has authored or co-authored numerous publications.
General Considerations.- The Constant Function c.- The Factorial Function n!.- The Zeta Numbers and Related Functions.- The Bernoulli Numbers B n .- The Euler Numbers E n .- The Binomial Coefficients .- The Linear Function bx + c and Its Reciprocal.- Modifying Functions.- The Heaviside u(x?a) And Dirac ?(x?a) Functions.- The Integer Powers x n And (bx+c) n .- The Square-Root Function and Its Reciprocal.- The Noninteger Powers x v .- The Semielliptic Function and Its Reciprocal.- The Semihyperbolic Functions And Their Reciprocals.- The Quadratic Function ax 2+bx+c and Its Reciprocal.- The Cubic Function x 3 + ax 2 + bx + c.- Polynomial Functions.- The Pochhammer Polynomials (x) n .- The Bernoulli Polynomials B n (x).- The Euler Polynomials E n (x).- The Legendre Polynomials P n (x).- The Chebyshev Polynomials T n (x) and U n (x).- The Laguerre Polynomials L n (x).- The Hermite Polynomials H n (x).- The Logarithmic Function ln(x).- The Exponential Function exp(±x).- Exponentials of Powers exp(± x v ).- The Hyperbolic Cosine Cosh(x) and Sine Sinh(x) Functions.- The Hyperbolic Secant Sech(x) and Cosecant Csch(x) Functions.- The Hyperbolic Tangent tanh(x) and Cotangent coth(x) Functions.- The Inverse Hyperbolic Functions.- The Cosine cos(x) and Sine sin(x) Functions.- The Secant sec(x) And cosecant csc(x) Functions.- The Tangent tan(x) and Cotangent cot(x) Functions.- The Inverse Circular Functions.- Periodic Functions.- The Exponential Integrals Ei(x) and Ein(x).- Sine and Cosine Integrals.- The Fresnel Integrals C(x) and S(x).- The Error Function erf(x) and Its Complement erfc(x).- The and Related Functions.- Dawson's Integral daw(x).- The Gamma Function ?(v).- The Digamma Function ?(v).- The Incomplete Gamma Functions.- The Parabolic Cylinder Function D v (x).- The Kummer Function M(a,c,x).- The Tricomi Function U(a,c,x).- The Modified Bessel Functions I n (x) of Integer Order.- The Modified Bessel Function I v (x) of Arbitrary Order.- The Macdonald Function K v (x).- The Bessel Functions J n (x) of Integer Order.- The Bessel Function J v (x) of Arbitrary Order.- The Neumann Function Y v (x).- The Kelvin Functions.- The Airy Functions Ai(x) and Bi(x).- The Struve Function h v (x).- The Incomplete Beta Function B(v,?,x).- The Legendre Functions P v (x) and Q v (x).- The Gauss Hypergeometric Function F(a,b,c,x).- The Complete Elliptic Integrals K(k) and E(k).- The Incomplete Elliptic Integrals F(k,?) AND E(k,?).- The Jacobian Elliptic Functions.- The Hurwitz Function ?(v, u).
