An Atlas of Functions

by Oldham, Keith B.; Myland, Jan; Spanier, Jerome

• ISBN13: 9780387488066
• ISBN10: 0387488065
• Edition: 2nd
• Format: Hardcover
• Copyright: 2008-11-11
• Publisher: Springer Verlag

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 all those 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, as well as many more. The 65 chapters are arranged roughly in order of increasing complexity, mathematical sophistication being kept to a minimum while utility is stressed 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 2 or 3 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 'œspecial''”that meet everyday needsa 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 calculusextensive cross-referencing and comprehensive indexing, with useful appendicesthe inclusion of innovative software--Equator, the Atlas Function Calculator--on a CD with the print book obviating the need for tables or programming to find numerical values (once installed onto your Windows-based PC, this unique function calculator generates precise function values on demand)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.

Author Biography

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.

Table of Contents

Preface

The Constant Function c

The Factorial Function n!

The Zeta Numbers and Related Functions

The Bernoulli Numbers Bn

The Euler Numbers En

The Bionmial Coefficients

The Linear Function bx + c and Its Reciprocal

Modifying Functions

The Heaviside and Dirac Functions

The Integer Powers xn and (bx + c)n

The Square-Root Function and Its Reciprocal

The Noninteger Power xv

The Semielliptic Function and Its Reciprocal

The (b/a)square root of x2 +- a2 Functions and Their Reciprocals

The Quadratic Function ax + bx + c and Its Reciprocal

The Cubic Function x3 + bx + c

Polynomial Functions

The Pochhammer Polynomials (x)n

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)

Exponential of Powers

The Hyperbolic Cosine cosh(x). and Sine sinh(x) Functions

The Hyperbolic Secant and Cosecant Functions

The Inverse Hyperbolic Functions

The Cosine cox(x) and Sine sin(x) Functions

The Secant sec(x) and Cosecant csc(x) Fucntions

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 of x) and Related Functions

Dawson's Integral daw(x)

The Gamma Function

The Digamma Function

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 Functions of In(x) Arbitrary Order

The Macdonald Function Kv(x)

The Bessel Functions Jn(x) of Integer Order

The Bessel Functions 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

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

The Jacobian Elliptic Functions

The Hurwitz Function

Useful Data

Bibliography

Equator, The Atlas Function Calculator

Symbol

Index

Subject

Index

Table of Contents provided by Publisher. All Rights Reserved.