View source for Book:Larry C. Andrews/Special Functions of Mathematics for Engineers

{{Book|Special Functions of Mathematics for Engineers|1992|McGraw-Hill|0-07-001848-0|Larry C. Andrews}}

=== Subject Matter ===

* [[Definition:Special Function|Special Functions]]

Second edition of {{BookLink|Special Functions for Engineers and Applied Mathematicians|Larry C. Andrews}} from 1985.


=== Contents ===

:Preface to the Second Edition
:Preface to the First Edition
:Notation for Special Functions

: Chapter 1. Infinite Series, Improper Integrals, and Infinite Products
:: 1.1 Introduction
:: 1.2 Infinite Series of Constants
::: 1.2.1 The Geometric Series
::: 1.2.2 Summary of Convergence Tests
::: 1.2.3 Operations wllh Series
::: 1.2.4 Factorials and Binomial Coefficients
:: 1.3 Infinite Series of Functions
::: 1.3.1 Properties of Uniformly Convergent Series
::: 1.3.2 Power Series
::: 1.3.3 Sums and Products of Power Series
:: 1.4 Fourier Trigonometric Series
::: 1.4.1 Cosine and Sine Series
:: 1.5 Improper Integrals
::: 1.5.1 Types of Improper Integrals
::: 1.5.2 Convergence Tests
::: 1.5.3 Pointwise and Uniform Convergence
:: 1.6 Asymptotic Formulas
::: 1.6.1 Small Arguments
::: 1.6.2 Large Arguments
:: 1.7 Infinite Products
::: 1.7.1 Associated Infinite Series
::: 1.7.2 Products of Functions

: Chapter 2. The Gamma Function and Related Functions
:: 2.1 Introduction
:: 2.2 Gamma Function
::: 2.2.1 Integral Representations
::: 2.2.2 Legendre Duplication Formula
::: 2.2.3 Weierstrass' Infinite Product
:: 2.3 Applications
::: 2.3.1 Miscellaneous Problems
::: 2.3.2 Fractional-Order Derivatives
:: 2.4 Beta Function
:: 2.5 Incomplete Gamma Function
::: 2.5.1 Asymptotic Series
:: 2.6 Digamma and Polygamma Functions
::: 2.6.1 Integral Representations
::: 2.6.2 Asymptotic Series
::: 2.6.3 Polygamma Functions
::: 2.6.4 Riemann Zeta Function

: Chapter 3. Other Functions Defined by Integrals
:: 3.1 Introduction
:: 3.2 Error Function and Related Functions
::: 3.2.1 Asymptotic Series
::: 3.2.2 Fresnel Integrals
:: 3.3 Applications
::: 3.3.1 Probability and Statistics
::: 3.3.2 Heat Conduction In Solids
::: 3.3.3 Vibrating Beams
:: 3.4 Exponential Integral and Related Functions
::: 3.4.1 Logarithmic Integral
::: 3.4.2 Sine and Cosine Integrals
:: 3.5 Elliptic Integrals
::: 3.5.1 Limiting Values and Series Representations
::: 3.5.2 The Pendulum Problem

: Chapter 4. Legendre Polynomials and Related Functions
:: 4.1 Introduction
:: 4.2 Legendre Polynomials
::: 4.2.1 The Generating Function
::: 4.2.2 Special Values and Recurrence Formulas
::: 4.2.3 Legendre's Differential Equation
:: 4.3 Other Representations of the Legendre Polynomials
::: 4.3.1 Rodrigues' Formula
::: 4.3.2 Laplace Integral Formula
::: 4.3.3 Some Bounds on $P_n(x)$
:: 4.4 Legendre Series
::: 4.4.1 Orthogonality of the Polynomials
::: 4.4.2 Finite Legendre Series
::: 4.4.3 Infinite Legendre Series
:: 4.5 Convergence of the Series
::: 4.5.1 Piecewise Continuous and Piecewise Smooth Functions
::: 4.5.2 Pointwise Convergence
:: 4.6 Legendre Functions of the Second Kind
::: 4.6.1 Basic Properties
:: 4.7 Associated Legendre Functions
::: 4.7.1 Basic Properties of $P_n^m(x)$
:: 4.8 Applications
::: 4.8.1 Electric Potential due to a Sphere
::: 4.8.2 Steady-State Temperatures In a Sphere

: Chapter 5. Other Orthogonal Polynomials
:: 5.1 Introduction
:: 5.2 Hermite Polynomials
::: 5.2.1 Recurrence Formulas
::: 5.2.2 Hermite Series
::: 5.2.3 Simple Harmonic Oscillator
:: 5.3 Laguerre Polynomials
::: 5.3.1 Recurrence Formulas
::: 5.3.2 Laguerre Series
::: 5.3.3 Associated Laguerre Polynomials
::: 5.3.4 The Hydrogen Atom
:: 5.4 Generalized Polynomial Sets
::: 5.4.1 Gegenbauer Polynomials
::: 5.4.2 Chebyshev Polynomials
::: 5.4.3 Jacobi Polynomials

: Chapter 6. Bessel Functions
:: 6.1 Introduction
:: 6.2 Bessel Functions of the First Kind
::: 6.2.1 The Generating Function
::: 6.2.2 Bessel Functions of Nonintegral Order
::: 6.2.3 Recurrence Formulas
::: 6.2.4 Bessel's Differential Equation
:: 6.3 Integral Representations
::: 6.3.1 Bessel's Problem
::: 6.3.2 Geometric Problems
:: 6.4 Integrals of Bessel Functions
::: 6.4.1 Indefinite Integrals
::: 6.4.2 Definite Integrals
:: 6.5 Series Involving Bessel Functions
::: 6.5.1 Addition Formulas
::: 6.5.2 Orthogonality of Bessel Functions
::: 6.5.3 Fourier-Bessel Series
:: 6.6 Bessel Functions of the Second Klnd
::: 6.6.1 Serles Expansion for $Y_n(x)$
::: 6.6.2 Asymptotic Formulas for Small Arguments
::: 6.6.3 Recurrence Formulas
:: 6.7 Differential Equations Related to Bessel's Equation
::: 6.7.1 The Oscillating Chaln

: Chapter 7. Bessel Functions of Other Kinds
:: 7.1 Introduction
:: 7.2 Modified Bessel Functions
::: 7.2.1 Modified Bessel Functions of the Second Kind
::: 7.2.2 Recurrence Formulas
::: 7.2.3 Generating Function and Addition Theorems
:: 7.3 Integral Relations
::: 7.3.1 Integral Representations
::: 7.3.2 Integrals of Modified Bessel Functions
:: 7.4 Spherical Bessel Functions
::: 7.4.1 Recurrence Formulas
::: 7.4.2 Modified Spherical Bessel Functions
:: 7.5 Other Bessel Functions
::: 7.5.1 Hankel Functions
::: 7.5.2 Struve Functions
::: 7.5.3 Kelvin's Functions
::: 7.5.4 Airy Functions
:: 7.6 Asymptotlc Formulas
::: 7.6.1 Small Arguments
::: 7.6.2 Large Arguments

: Chapter 8. Applications Involving Bessel Functions
:: 8.1 Introductions
:: 8.2 Problems in Mechanics
::: 8.2.1 The Lengthening Pendulum
::: 8.2.2 Buckling of a Long Column
:: 8.3 Statistical Communication Theory
::: 8.3.1 Narrowband Nolse and Envelope Detection
::: 8.3.2 Non-Rayleigh Radar Sea Clutter
:: 8.4 Heat Conduction and Vibration Phenomena
::: 8.4.1 Radial Symmetric Problems Involving Circles
::: 8.4.2 Radial Symmetric Problems Involving Cylinders
::: 8.4.3 The Helmholtz Equatlon
:: 8.5 Step-Index Optical Fibers

: Chapter 9. The Hypergeometric Function
:: 9.1 Introduction
:: 9.2 The Pochhammer Symbol
:: 9.3 The Function $F(a, b; c; x)$
::: 9.3.1 Elementary Properties
::: 9.3.2 Integral Representation
::: 9.3.3 The Hypergeometric Equation
:: 9.4 Relation to Other Functions
::: 9.4.1 Legendre Functions
:: 9.5 Summing Series and Evaluating Integrals
::: 9.5.1 Action-Angle Variables

: Chapter 10. The Confluent Hypergeometric Functions
:: 10.1 Introduction
:: 10.2 The Functions $M(a; c; x)$ and $U(a; c; x)$
::: 10.2.1 Elementary Properties of $M(a; c; x)$
::: 10.2.2 Confluent Hypergeometric Equation and $U(a; c; x)$
::: 10.2.3 Asymptotic Formulas
:: 10.3 Relation to Other Functions
::: 10.3.1 Hermite Functions
::: 10.3.2 Laguerre Functions
:: 10.4 Whittaker Functions

: Chapter 11. Generalized Hypergeometric Functions
:: 11.1 Introduction
:: 11.2 The Set of Functions ${}_pF_q$
::: 11.2.1 Hypergeometric-Type Series
:: 11.3 Other Generalizations
::: 11.3.1 The Meijer $G$ Function
::: 11.3.2 The MacRobert $E$ Function

: Chapter 12. Applications Involving Hypergeometric-Type Functions
:: 12.1 Introduction
:: 12.2 Statistical Communication Theory
::: 12.2.1 Nonlinear Devices
:: 12.3 Fluid Mechanics
::: 12.3.1 Unsteady Hydrodynamic Flow Past an Infinite Plate
::: 12.3.2 Transonic Flow and the Euler-Tricomi Equation
:: 12.4 Random Fields
::: 12.4.1 Structure Function of Temperature

: Bibliography
: Appendix: A List of Special Function Formulas
: Selected Answers to Exercises

:: Index

[[Category:Books/Special Functions]]