目次

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.


Sample Pages(PDF)



Table of 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 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
　　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 Function of the First Kind
　　Properties of Bessel Functions of the First Kind
　　Bessel Function of the Second Kind
　　Properties of Bessel Functions of the Second Kind
　　Modified Bessel Function of the First Kind
　　Properties of Modified Bessel Functions of the First Kind
　　Modified Bessel Function of the Second Kind
　　Properties of Modified Bessel Functions of the Second Kind
　　Spherical Bessel Functions
　　Properties of Spherical Bessel Functions
　　Modified Spherical Bessel Functions
　　Hankel Functions
　　Struve Functions
　　Kelvin's Functions
　　Airy Functions
　　Other Related 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
　　Confluent Hypergeometric Functions
　　Confluent Hypergeometric Function Identities
　　Generalized Hypergeometric Function
　　Hypergeometric Function Example
　　Confluent Hypergeometric Function Example
　　Relation 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