Field guide to special functions for engineers / Larry C. Andrews.

Format:

Book

Author/Creator:

Andrews, Larry C., author.

Contributor:

Society of Photo-Optical Instrumentation Engineers.

Series:

SPIE field guides ; FG18.

SPIE digital library

The field guide series ; 18

Language:

English

Subjects (All):

Engineering mathematics--Formulae--Handbooks, manuals, etc.

Engineering mathematics.

Engineering mathematics--Formulae.

Genre:

Handbooks and manuals.

Electronic books.

Physical Description:

1 online resource (106 unnumbered pages) : digital file.

Place of Publication:

Bellingham, Wash. : SPIE, 2011.

System Details:

Mode of access: World Wide Web.

text file

Summary:

This Field Guide is designed to provide engineers and scientists with a quick reference for special functions that are crucial to resolving modern engineering and physics problems. The functions treated in this book apply to many fields, including electro-optics, electromagnetic theory, wave propagation, heat conduction, quantum mechanics, probability theory, and electric circuit theory, among many other areas of application. A brief review of these important topics is included in this guide, as well as an introduction to some useful engineering functions such as the step function, rectangle function, and delta (impulse) function.

Contents:

Glossary of symbols and notation

Engineering functions

Step and signum (sign) functions

Rectangle and triangle functions

Sinc and Gaussian functions

Delta function

Delta function example

Comb function

Infinite series and improper integrals

Series of constants

Operations with series

Factorials and binomial coefficients

Factorials and binomial coefficients example

Power series

Operations with power series

Power series example

Improper integrals

Asymptotic series for small arguments

Asymptotic series for large arguments

Asymptotic series example

Gamma functions

Integral representations

Gamma function identities

Incomplete gamma functions

Incomplete gamma function identities

Gamma function example

Beta function

Gamma and beta function example

Digamma (Psi) and polygamma functions

Asymptotic series

Bernoulli numbers and polynomials

Riemann zeta function

Other functions defined by integrals

Error functions

Fresnel integrals

Exponential and logarithmic integrals

Sine and cosine integrals

Elliptic integrals

Elliptic functions

Cumulative distribution function example

Orthogonal polynomials

Legendre polynomials

Legendre polynomial identities

Legendre functions of the second kind

Associated Legendre functions

Spherical harmonics

Hermite polynomials

Hermite polynomial identities

Hermite polynomial example

Laguerre polynomials

Laguerre polynomial identities

Associated Laguerre polynomials

Chebyshev polynomials

Chebyshev polynomial identities

Gegenbauer polynomials

Jacobi polynomials

Bessel functions

Bessel functions of the first kind

Properties of Bessel functions of the first kind

Bessel functions of the second kind

Properties of Bessel functions of the second kind

Modified Bessel functions of the first kind

Properties of the modified Bessel functions of the first kind

Modified Bessel functions of the second kind

Properties of the modified Bessel functions of the second kind

Spherical Bessel functions

Properties of the spherical Bessel functions

Modified spherical Bessel functions

Hankel functions

Struve functions

Kelvin's functions

Airy functions

Other Bessel functions

Differential equation example

Bessel function example

Orthogonal series

Fourier trigonometric series

Fourier trigonometric series: general intervals

Exponential Fourier series

Generalized Fourier series

Fourier series example

Legendre series

Hermite and Laguerre series

Bessel series

Bessel series example

Hypergeometric-type functions

Pochhammer symbol

Hypergeometric function

Hypergeometric function identities

Hypergeometric function example

Confluent hypergeometric functions

Confluent hypergeometric function identities

Confluent hypergeometric function example

Generalized hypergeometric functions

Relations of pFq to other functions

Meijer G function

Properties of the Meijer G function

Relation of the G function to other functions

MacRobert E function

Meijer G example

Bibliography

Index.

Notes:

"SPIE Digital Library."--Website.

Includes bibliographical references.

Title from PDF title page (SPIE eBooks Website, viewed 2011-04-25).

Other Format:

Print version:

ISBN:

9780819485519

OCLC:

714897590

Access Restriction:

Restricted for use by site license.