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.
- Appendix A: Useful Data.
- Appendix B: Bibliography.
- Appendix C: Equator, The Atlas Function Calculator.
- Symbol Index.
- Subject Ind
By:
Keith B. Oldham,
Jan Myland,
Jerome Spanier
Imprint: Springer-Verlag New York Inc.
Country of Publication: United States
Edition: Softcover reprint of the original 2nd ed. 2009
Dimensions:
Height: 279mm,
Width: 210mm,
Weight: 2.623kg
ISBN: 9781493950584
ISBN 10: 1493950584
Pages: 748
Publication Date: 23 August 2016
Audience:
Professional and scholarly
,
Undergraduate
Format: Paperback
Publisher's Status: Active
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).
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.
Reviews for An Atlas of Functions: with Equator, the Atlas Function Calculator
"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)"
