http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Field guide to special functions for engineers
Society of Photo-optical Instrumentation Engineers
1 online resource (106 unnumbered pages)
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.
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 --
Engineering functions -- Step and signum (sign) functions -- Rectangle and triangle functions -- Sinc and Gaussian functions -- Delta function -- Delta function example -- Comb function --
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 --
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 --
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 --
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 --
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 --
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 --
Restricted to subscribers or individual electronic text purchasers.
System requirements: Adobe Acrobat Reader.