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.
Author(s): Keit Oldham, Jan Myland, Jerome Spanier (auth.)
Edition: 2
Publisher: Springer-Verlag New York
Year: 2009
Language: English
Pages: 750
Tags: Applications of Mathematics;Special Functions;Real Functions;Theoretical, Mathematical and Computational Physics;Computational Intelligence
Front Matter....Pages i-xi
General Considerations....Pages 1-11
The Constant Function c ....Pages 13-19
The Factorial Function n !....Pages 21-27
The Zeta Numbers and Related Functions....Pages 29-38
The Bernoulli Numbers B n ....Pages 39-44
The Euler Numbers E n ....Pages 45-48
The Binomial Coefficients $\left( {_m^v } \right)$ ....Pages 49-56
The Linear Function bx + c and Its Reciprocal....Pages 57-65
Modifying Functions....Pages 67-74
The Heaviside u( x − a ) And Dirac δ( x − a ) Functions....Pages 75-80
The Integer Powers x n And ( bx + c ) n ....Pages 81-93
The Square-Root Function $\sqrt {bx + c}$ and Its Reciprocal....Pages 95-102
The Noninteger Powers x v ....Pages 103-112
The Semielliptic Function $\left( {b/a} \right)\sqrt {a^2 {\kern 1pt} - x^2 }$ and Its Reciprocal....Pages 113-120
The Semihyperbolic Functions $\left( {b/a} \right)\sqrt {x^2 {\kern 1pt} \pm a^2 }$ And Their Reciprocals....Pages 121-130
The Quadratic Function ax 2 + bx + c and Its Reciprocal....Pages 131-138
The Cubic Function x 3 + ax 2 + bx + c ....Pages 139-146
Polynomial Functions....Pages 147-158
The Pochhammer Polynomials ( x ) n ....Pages 159-174
The Bernoulli Polynomials B n ( x )....Pages 175-180
The Euler Polynomials E n ( x )....Pages 181-186
The Legendre Polynomials P n ( x )....Pages 187-196
The Chebyshev Polynomials T n ( x ) and U n ( x )....Pages 197-208
The Laguerre Polynomials L n ( x )....Pages 209-216
The Hermite Polynomials H n ( x )....Pages 217-227
The Logarithmic Function ln( x )....Pages 229-239
The Exponential Function exp(± x )....Pages 241-253
Exponentials of Powers exp(± x v )....Pages 255-267
The Hyperbolic Cosine Cosh( x ) and Sine Sinh( x ) Functions....Pages 269-279
The Hyperbolic Secant Sech( x ) and Cosecant Csch( x ) Functions....Pages 281-288
The Hyperbolic Tangent tanh( x ) and Cotangent coth( x ) Functions....Pages 289-296
The Inverse Hyperbolic Functions....Pages 297-307
The Cosine cos( x ) and Sine sin( x ) Functions....Pages 309-328
The Secant sec( x ) And cosecant csc( x ) Functions....Pages 329-338
The Tangent tan( x ) and Cotangent cot( x ) Functions....Pages 339-350
The Inverse Circular Functions....Pages 351-366
Periodic Functions....Pages 367-374
The Exponential Integrals Ei( x ) and Ein( x )....Pages 375-383
Sine and Cosine Integrals....Pages 385-394
The Fresnel Integrals C( x ) and S( x )....Pages 395-404
The Error Function erf( x ) and Its Complement erfc( x )....Pages 405-415
The $\exp \left( x \right){\mathop{\rm erfc}\nolimits} \left( {\sqrt x } \right)$ and Related Functions....Pages 417-426
Dawson’s Integral daw( x )....Pages 427-433
The Gamma Function Γ( v )....Pages 435-448
The Digamma Function ψ( v )....Pages 449-460
The Incomplete Gamma Functions....Pages 461-470
The Parabolic Cylinder Function D v ( x )....Pages 471-484
The Kummer Function M( a , c , x )....Pages 485-496
The Tricomi Function U( a , c , x )....Pages 497-506
The Modified Bessel Functions I n ( x ) of Integer Order....Pages 507-517
The Modified Bessel Function I v ( x ) of Arbitrary Order....Pages 519-526
The Macdonald Function K v ( x )....Pages 527-536
The Bessel Functions J n ( x ) of Integer Order....Pages 537-552
The Bessel Function J v ( x ) of Arbitrary Order....Pages 553-565
The Neumann Function Y v ( x )....Pages 567-576
The Kelvin Functions....Pages 577-584
The Airy Functions Ai( x ) and Bi( x )....Pages 585-592
The Struve Function h v ( x )....Pages 593-601
The Incomplete Beta Function B( v ,μ, x )....Pages 603-609
The Legendre Functions P v ( x ) and Q v ( x )....Pages 611-626
The Gauss Hypergeometric Function F( a , b , c , x )....Pages 627-636
The Complete Elliptic Integrals K( k ) and E( k )....Pages 637-651
The Incomplete Elliptic Integrals F( k ,ϕ) AND E( k ,ϕ)....Pages 653-669
The Jacobian Elliptic Functions....Pages 671-684
The Hurwitz Function ζ( v , u )....Pages 685-695
Back Matter....Pages 697-748
