Special Functions for Scientists and Engineers

ISBN-10: 0486435210

ISBN-13: 9780486435213

Edition: 2004

Authors: W. W. Bell
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Description: Clear and comprehensive, this text provides undergraduates with a straightforward guide to special functions. It is equally suitable as a reference volume for professionals, and readers need no higher level of mathematical knowledge beyond elementary calculus. Topics include the solution of second-order differential equations in terms of power series; gamma and beta functions; Legendre polynomials and functions; Bessel functions; Hermite, Laguerre, and Chebyshev polynomials; Gegenbauer and Jacobi polynomials; and hypergeometric and other special functions. Three appendices offer convenient tabulation of principal results, and a generous supply of worked examples and problems includes some hints and solutions. 1968 ed. 25 figures.

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Book details

List price: $18.95
Copyright year: 2004
Publisher: Dover Publications, Incorporated
Publication date: 7/26/2004
Binding: Paperback
Pages: 272
Size: 5.25" wide x 8.50" long x 0.75" tall
Weight: 0.638
Language: English

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Preface
List of Symbols
Series Solution of Differential Equations
Method of Frobenius
Examples
Problems
Gamma and Beta Functions
Definitions
Properties of the beta and gamma functions
Definition of the gamma function for negative values of the argument
Examples
Problems
Legendre Polynomials and Functions
Legendre's equation and its solution
Generating function for the Legendre polynomials
Further expressions for the Legendre polynomials
Explicit expressions for and special values of the Legendre polynomials
Orthogonality properties of the Legendre polynomials
Legendre series
Relations between the Legendre polynomials and their derivatives; recurrence relations
Associated Legendre functions
Properties of the associated Legendre functions
Legendre functions of the second kind
Spherical harmonics
Graphs of the Legendre functions
Examples
Problems
Bessel Functions
Bessel's equation and its solutions; Bessel functions of the first and second kind
Generating function for the Bessel functions
Integral representations for Bessel functions
Recurrence relations
Hankel functions
Equations reducible to Bessel's equation
Modified Bessel functions
Recurrence relations for the modified Bessel functions
Integral representations for the modified Bessel functions
Kelvin's functions
Spherical Bessel functions
Behaviour of the Bessel functions for large and small values of the argument
Graphs of the Bessel functions
Orthonormality of the Bessel functions; Bessel series
Integrals involving Bessel functions
Examples
Problems
Hermite Polynomials
Hermite's equation and its solution
Generating function
Other expressions for the Hermite polynomials
Explicit expressions for, and special values of, the Hermite polynomials
Orthogonality properties of the Hermite polynomials
Relations between Hermite polynomials and their derivatives; recurrence relations
Weber-Hermite functions
Examples
Problems
Laguerre Polynomials
Laguerre's equation and its solution
Generating function
Alternative expression for the Laguerre polynomials
Explicit expressions for, and special values of, the Laguerre polynomials
Orthogonality properties of the Laguerre polynomials
Relations between Laguerre polynomials and their derivatives; recurrence relations
Associated Laguerre polynomials
Properties of the associated Laguerre polynomials
Notation
Examples
Problems
Chebyshev Polynomials
Definition of Chebyshev polynomials; Chebyshev's equation
Generating function
Orthogonality properties
Recurrence relations
Examples
Problems
Gegenbauer and Jacobi Polynomials
Gegenbauer polynomials
Jacobi polynomials
Examples
Problems
Hypergeometric Functions
Definition of hypergeometric functions
Properties of the hypergeometric function
Properties of the confluent hypergeometric function
Examples
Problem
Other Special Functions
Incomplete gamma functions
Exponential integral and related functions
The error function and related functions
Riemann's zeta function
Debye functions
Elliptic integrals
Examples
Problems
Appendices
Convergence of Legendre series
Euler's constant
Differential equations
Orthogonality relations
Generating functions
Hints and Solutions to Problems
Bibliography
Index
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