An Atlas of Functions

with Equator, the Atlas Function Calculator
2. Auflage 2009
ISBN: 978-1-4939-5058-4
Verlag: Springer

Buch, Englisch, 748 Seiten, Previously published in hardcover, Format (B × H): 210 mm x 279 mm, Gewicht: 1826 g

Reihe: An Atlas of Functions

Modernized and upgraded edition of a valuable reference work first published in 1987 Uses the language of mathematics that is common to all branches of science and engineering Print volume includes the inclusion of innovative software--Equator, the Atlas Function Calculator. This software obviates the need for tables or programming to find numerical values (once installed onto your Windows XP based PC, this unique function calculator instantly generates precise function values on demand) Provides comprehensive information in 65 chapters on several hundred functions or function families of interest to scientists, engineers and mathematicians Information arranged by topics in order of complexity Mathematical sophistication kept at a minimum; utility and applications stressed throughout Enhanced by color figures in 2 or 3 dimensions Includes supplementary material: sn.pub/extras

Zielgruppe

Research

Autoren/Hrsg.

Oldham, Keith B.

Myland, Jan

Spanier, Jerome

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz

Inhaltsverzeichnis

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).

Über Autor(innen)

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.