Research Catalog

Title

Atlas for computing mathematical functions : an illustrated guide for practitioners, with programs in C and Mathematica / William J. Thompson.

Author

Thompson, William J. (William Jackson), 1939-

Publication

New York : Wiley, c1997.

Items in the Library & Off-site

Details

Description

xiv, 903 p. : ill.; 26 cm. +

Subject

• Functions > Computer programs
• Science > Mathematics > Computer programs
• C (Computer program language)
• Mathematica (Computer program language)

Note

• "A Wiley-Interscience publication."

Bibliography (note)

• Includes bibliographical references and indexes.

System Details (note)

• System requirements: Windows or Macintosh.

Processing Action (note)

• committed to retain

Contents

The atlas of functions : What this atlas contains ; How to use the atlas ; About the production of the atlas. The computer interface : What the CD-ROM contains ; How to locate a function ; Exploring functions with Mathematica ; The c functions: no assembly required ; Hints for Fortran and Pascal programmers ; File names for pc-based systems ; Reliability of programs: disclaimer ; References on the computer interface. The functions : Introduction to the functions : How the function descriptions are organized -- A visual tour of the atlas -- Computing strategies : General computing strategies ; Iteration and recursion ; Continued fractions and rational approximations ; Using asymptomatic expansions ; Euler-Maclaurin summation formula ; Accuracy and precision of the functions ; Mathematical constants used in the atlas -- Elementary transcendental functions : Exponential and logarithmic functions : Exponentials ; Logarithms. Circular and inverse circular functions : Circular functions ; Inverse circular functions. Hyperbolic and inverse hyperbolic functions : Hyperbolic functions ; Inverse hyperbolic functions -- Exponential integrals and related functions : Exponential and logarithmic integrals : Exponential integral of the first kind ; Exponential integral of the second kind ; Logarithmic integral. Cosine and sine integrals -- Gamma and beta functions : Gamma function and beta function : Gamma function ; Beta function. Psi (digamma) and polygamma functions : Psi function ; Polygamma functions. Incomplete gamma and beta functions : Incomplete gamma function ; Incomplete beta function -- Combinatorial functions : Factorials and rising factorials : Factorial function ; Rising factorial function. Binominal and multinominal coefficients : Binominal coefficients ; Multinominal coefficients. Stirling numbers of first and second kinds : Stirling numbers of the first kind ; Stirling numbers of the second kind. Fibonacci and Lucas polynomials : Fibonacci polynomials and Fibonacci numbers ; Lucas polynomials and Lucas numbers -- Number theory functions : Bernoulli numbers and Bernoulli polynomials : Bernoulli numbers ; Bernoulli polynomials. Euler numbers and Euler polynomials : Euler numbers ; Euler polynomials. Riemann zeta function ; Other sums of reciprocal powers ; Polylogarithms -- Probability distributions : Overview of probability distribution functions ; Discrete probability distributions : Binomial distribution ; Negative binomial (Pascal) distribution ; Geometric distribution ; Hypergeometric distribution ; Logarithmic series distribution ; Poisson distribution. Normal probability distributions : Gauss (normal) probability function ; Bivariate normal probability function ; Chi-square probability functions ; F-(variance-ratio) distribution functions ; Student’s t-distribution functions ; Lognormal distribution. Other continuous probability distributions : Cauchy (Lorentz) distribution ; Exponential distribution ; Pareto distribution ; Weibull distribution ; Logistic distribution ; Laplace distribution ; Kolmogorov-Smirnov distribution ; Beta distribution -- Error function, Fresnel and Dawson integrals : Error function ; Fresnel integrals ; Dawson integral -- Orthogonal polynomials : Overview of orthogonal polygons ; Chebyshev polynomials : Chebyshev polynomials of the first kind ; Chebyshev polynomials of the second kind. Gegenbauer (ultraspherical) polynomials ; Hermite polynomials ; Laguerre polynomials ; Legendre polynomials ; Jacobi polynomials -- Legendre Functions : Overview of Legendre functions : Visualizing Legendre functions of the first kind ; Visualizing Legendre functions of the second kind ; Legendre functions and coordinate systems. Spherical Legendre functions : Spherical polar coordinates ; Legendre functions of the first kind for integer m and n ; Legendre functions of the second kind for integer m and n. Toroidal Legendre functions : Toroidal coordinates ; Toroidal functions of the first kind ; Toroidal functions of the second kind. Conical Legendre functions : Laplace equation on a cone ; Conical functions -- Spheroidal wave functions : Overview of spheroidal wave functions : Spheroidal coordinates ; Scalar wave equation in spheroidal coordinates ; Eigenvalues for spheroidal equations ; Auxiliary functions for eigenvalues. Spheroidal angular functions : Expansion coefficients for angular functions ; Spheroidal angular functions. Spheroidal radial functions : Expansion coefficients for radial functions ; Spheroidal radial functions -- Bessel Functions : Overview of Bessel functions ; Bessel functions of integer order : Regular cylindrical Bessel function ; Irregular cylindrical Bessel function ; Regular hyperbolic Bessel function ; Irregular hyperbolic Bessel function. Kelvin functions : Regular Kelvin functions ; Irregular Kelvin functions. Bessel functions of half-integer order : Regular spherical Bessel function ; Irregular spherical Bessel function ; Regular modified spherical Bessel function ; Irregular modified spherical Bessel function. Airy functions : Airy functions ; Derivatives of Airy functions -- Struve, anger, and weber functions : Struve functions : Struve function ; Modified Struve function. Anger and weber functions : Overview of anger and weber functions ; Anger function ; Weber function -- Hypergeometric functions and coulomb wave functions : Hypergeometric functions ; Confluent hypergeometric functions : Regular function ; Irregular function. Coulomb wave functions : Regular functions and derivatives ; Irregular functions and derivatives -- Elliptic integrals and elliptic functions : Overview of elliptic integrals and elliptic functions ; Elliptic integrals : Elliptic integrals of the first kind ; Elliptic integrals of the second kind ; Jacobi zeta function ; Heuman lambda function ; Elliptic integrals of the third kind. Jacobi elliptic functions and theta functions : Jacobi elliptic functions ; Theta functions ; Logarithmic derivatives of theta functions -- Parabolic cylinder functions : Parabolic cylinder coordinates ; Parabolic cylinder functions : Parabolic cylinder functions U ; Parabolic cylinder functions V -- Miscellaneous functions for science and engineering : Debye functions ; Sievert integral ; Abramowitz function ; Spence integral ; Clausen integral ; Voigt (plasma dispersion) function ; Angular momentum coupling coefficients : 3-j coefficients ; 6-j coefficients ; 9-j coefficients -- The computer interface : The Mathematica notebooks : Introduction to the notebooks ; Exploring with the notebook cells ; The annotated notebooks ; Elementary transcendental functions ; Exponential integrals and related functions ; Gamma and beta functions ; Combinatorial functions ; Number theory functions ; Probability distributions ; Error function, Fresnel and Dawson integrals ; Orthogonal polynomials ; Legendre functions ; Spheroidal wave functions ; Bessel functions ; Struve, anger, and weber-functions ; Hypergeometric functions and Coulomb wave functions ; Elliptic integrals and elliptic functions ; Parabolic cylinder functions ; Miscellaneous functions for science and engineering -- The c driver programs : Introduction to the c driver programs ; How the c drivers are organized ; Annotations to the c driver programs ; Elementary transcendental functions : Exponential and logarithmic functions ; Circular and inverse circular functions ; Hyperbolic and inverse hyperbolic functions. Exponential integrals and related functions : Exponential and logarithmic integrals ; Cosine and sine integrals. Gamma and beta functions : Gamma function and beta function ; Psi (digamma) and polygamma functions ; Incomplete gamma and beta functions. Combinatorial functions : Factorials and rising factorials ; Binomial and multinomial coefficients ; Stirling numbers of the first and second kinds ; Fibonacci and Lucas polynomials. Number theory functions : Bernoulli numbers and Bernoulli polynomials ; Euler numbers and Euler polynomials ; Riemann zeta function ; Other sums of reciprocal powers ; Polylogarithms. Probability distributions : Organization of the PDFs ; Discrete probability distributions ; Normal probability distributions ; Other continuous probability distributions. Error function, Fresnel and Dawson integrals : Error function ; Fresnel integrals ; Dawson integral. Orthogonal polynomials : Orthogonal polynomial functions ; Chebyshev polynomials ; Gegenbauer (ultraspherical) polynomials ; Hermite polynomials ; Laguerre polynomials ; Legendre polynomials ; Jacobi polynomials. Legendre functions : Overview of Legendre functions ; Spherical Legendre functions ; Toroidal Legendre functions ; Conical Legendre functions. Spheroidal wave functions : Overview of Bessel functions ; Bessel functions of integer order ; Kelvin functions ; Bessel functions of half-integer order ; Airy functions. Struve, anger, and weber functions : Struve functions ; Anger and weber functions. Hypergeometric functions ; Confluent hypergeometric functions ; Coulomb wave functions. Elliptic integrals and elliptic functions : Overview of elliptic integrals and elliptic functions ; Elliptic integrals ; Jacobi elliptic functions and theta functions. Parabolic cylinder functions. Miscellaneous functions for science and engineering : Debye functions ; Sievert integral ; Abramowitz function ; Spence integral ; Clausen integral ; Voigt (plasma dispersion) function ; Angular momentum coupling coefficients.

ISBN

0471002607 (cloth : alk. paper)

LCCN

^^^96032557^//r97

OCLC

• 35192264
• SCSB-10400013

Owning Institutions

Harvard Library