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Book Cover
E-book
Author Oldham, Keith B

Title An atlas of functions : with Equator, the atlas function calculator / Keith Oldham, Jan Myland, & Jerome Spanier. ©1987
Edition Second edition
Published New York, NY : Springer, [2009]
©2009

Copies

Description 1 online resource (xi, 748 pages) : color illustrations
Contents General considerations -- The constant function c -- The factorial function n! -- The zeta numbers and related functions -- The Bernoulli numbers Bn -- The Euler numbers En -- The binomial coefficients (v[over]m) -- The linear function bx+c and its reciprocal -- Modifying functions -- The Heaviside u(x-a) and Dirac [delta](x-a) functions -- The integer powers x[superscript]n and (bx+c)[superscript]n -- The square-root function [square root]bx+c and its reciprocal -- The noninteger powers x[superscript]v -- The semielliptic function b/a [square root]a[superscript]2x[superscript]2 and its reciprocal -- The semihyperbolic functions b/a [square root]x[superscript]2±a[superscript]2 and their reciprocals -- The quadratic function ax2 + bx + c and its reciprocal -- The cubic function x[superscript]3+ax[superscript]2+bx+c -- Polynomial functions -- The Pochhammer polynomials (x) -- The Bernoulli polynomials Bn(x) -- The Euler polynomials En(x) -- The Legendre polynomials Pn(x) -- The Chebyshev polynomials Tn(x) AND Un(x) -- The Laguerre polynomials Ln(x) -- The Hermite polynomials Hn(x) -- The logarithmic function ln(x) -- The exponential function exp(± x) -- Exponentials of powers exp(± x[superscript]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 exp(x)erfc [square root]x and related functions -- Dawson's integral daw(x) -- The gamma function [gamma](v) -- The digamma function [psi](v) -- The incomplete gamma functions -- The parabolic cylinder function Dv(x) -- The Kummer function M(a, c, x) -- The Tricomi function U(a, c, x) -- The modified Bessel functions In(x) of integer order -- The modified Bessel function Iv(x) of arbitrary order -- The Macdonald function Kv(x) -- The Bessel functions Jn(x) of integer order -- The Bessel function Jv(x) of arbitrary order -- The Neumann function Yv(x) -- The Kelvin functions -- The Airy functions Ai(x) AND Bi(x) -- The Struve function hv(x) -- The incomplete beta function B(v, [mu], x) -- The Legendre functions Pv(x) and Qv(x) -- The Gauss hypergeometric function F(a, b, c, x) -- The complete elliptic integrals K(k) and E(k) -- The incomplete elliptic integrals F([kappa], [phi]) and E([kappa], [phi]) -- The Jacobian elliptic functions -- The Hurwitz function [xi](v, u) -- Appendices. Useful data -- Bibliography -- Equator, the atlas function calculator
Summary This second edition of An Atlas of Functions, with Equator, the Atlas Function Calculator, provides comprehensive information on several hundred functions or function families of interest to scientists, engineers and mathematicians who are concerned with the quantitative aspects of their field. Beginning with simple integer-valued functions, the book progresses to polynomials, exponential, trigonometric, Bessel, and hypergeometric functions, and many more. The 65 chapters are arranged roughly in order of increasing complexity, mathematical sophistication being kept to a minimum while stressing utility throughout. In addition to providing definitions and simple properties for every function, each chapter catalogs more complex interrelationships as well as the derivatives, integrals, Laplace transforms and other characteristics of the function. Numerous color figures in two- or three- dimensions depict their shape and qualitative features and flesh out the reader's familiarity with the functions. In many instances, the chapter concludes with a concise exposition on a topic in applied mathematics associated with the particular function or function family. Features that make the Atlas an invaluable reference tool, yet simple to use, include: full coverage of those functions--elementary and "special"--That meet everyday needs a standardized chapter format, making it easy to locate needed information on such aspects as: nomenclature, general behavior, definitions, intrarelationships, expansions, approximations, limits, and response to operations of the calculus extensive cross-referencing and comprehensive indexing, with useful appendices the inclusion of innovative software--Equator, the Atlas Function Calculator the inclusion of new material dealing with interesting applications of many of the function families, building upon the favorable responses to similar material in the first edition
Notes Revised edition of: An atlas of functions / Jerome Spanier, Keith B. Oldham. ©1987
Bibliography Includes bibliographical references and indexes
Notes Online resource; title from electronic title page (EBSCOhost, viewed April 4, 2018)
In Springer eBooks
Subject Functions.
functions (mathematics)
MATHEMATICS -- Calculus.
MATHEMATICS -- Mathematical Analysis.
Functions
Funktion Mathematik
Mathematik
Functies (wiskunde)
Genre/Form Naslagwerken (vorm)
Form Electronic book
Author Myland, Jan C
Spanier, Jerome, 1930-
Preceded by: Spanier, Jerome, 1930- An atlas of functions. ©1987
LC no. 2008937525 2008929330
ISBN 9780387488073
0387488073
9780387496146
0387496149