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Special functions of mathematics for engineers

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Special functions of mathematics for engineers/ Larry C. Andrews.
作者:	Andrews, Larry C.
出版者:	Bellingham, Wash. (1000 20th St. Bellingham WA 98225-6705 USA) :SPIE, : 1998.,
面頁冊數:	1 online resource (xvii, 479 p. : ill.) :digital file. :
附註:	"SPIE digital library."
標題:	Functions, Special. -
電子資源:	http://dx.doi.org/10.1117/3.270709
ISBN:	9780819478467 (electronic)

Special functions of mathematics for engineers
Andrews, Larry C.

Special functions of mathematics for engineers[electronic resource] /Larry C. Andrews. - 2nd ed. - Bellingham, Wash. (1000 20th St. Bellingham WA 98225-6705 USA) :SPIE,1998. - 1 online resource (xvii, 479 p. : ill.) :digital file. - SPIE Press monograph ;PM49. - SPIE Press monograph ;PM103..

"SPIE digital library."

Includes bibliographical references (p. 451) and index.

Chapter 1. Infinite series, improper integrals, and infinite products -- Introduction -- Infinite series of constants -- The geometric series -- Summary of convergence tests -- Operations with series -- Factorials and binomial coefficients -- Infinite series of functions -- Properties of uniformly convergent series -- Power series -- Sums and products of power series -- Fourier trigonometric series -- Cosine and sine series -- Improper integrals -- Types of improper integrals -- Convergence tests -- Pointwise and uniform convergence -- Asymptotic formulas -- Small arguments -- Large arguments -- Infinite products -- Associated infinite series -- Products of functions.

Restricted to subscribers or individual electronic text purchasers.

Modern engineering and physical science applications demand a thorough knowledge of applied mathematics, particularly special functions. These typically arise in applications such as communication systems, electro-optics, nonlinear wave propagation, electromagnetic theory, electric circuit theory, and quantum mechanics. This text systematically introduces special functions and explores their properties and applications in engineering and science.

System requirements: Adobe Acrobat Reader.

ISBN: 9780819478467 (electronic)

Standard No.: 10.1117/3.270709doiSubjects--Topical Terms:

527750
Functions, Special.

LC Class. No.: QA351 / .A75 1998e

Dewey Class. No.: 515/.5

Special functions of mathematics for engineers
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245 1 0 $a Special functions of mathematics for engineers $h [electronic resource] / $c Larry C. Andrews.
250 $a 2nd ed.
260 $a Bellingham, Wash. (1000 20th St. Bellingham WA 98225-6705 USA) : $b SPIE, $c 1998.
300 $a 1 online resource (xvii, 479 p. : ill.) : $b digital file.
490 1 $a SPIE Press monograph ; $v PM49
500 $a "SPIE digital library."
500 $a Copublished with Oxford University Press.
500 $a Originally published: 2nd ed. New York : McGraw-Hill, c1992.
504 $a Includes bibliographical references (p. 451) and index.
505 0 $a Chapter 1. Infinite series, improper integrals, and infinite products -- Introduction -- Infinite series of constants -- The geometric series -- Summary of convergence tests -- Operations with series -- Factorials and binomial coefficients -- Infinite series of functions -- Properties of uniformly convergent series -- Power series -- Sums and products of power series -- Fourier trigonometric series -- Cosine and sine series -- Improper integrals -- Types of improper integrals -- Convergence tests -- Pointwise and uniform convergence -- Asymptotic formulas -- Small arguments -- Large arguments -- Infinite products -- Associated infinite series -- Products of functions.
505 0 $a Chapter 2. The gamma function and related functions -- Introduction -- Gamma function -- Integral representations -- Legendre duplication formula -- Weierstrass' infinite product -- Applications -- Miscellaneous problems -- Fractional-order derivatives -- Beta function -- Incomplete gamma function -- Asymptotic series -- Digamma and polygamma functions -- Integral representations -- Asymptotic series -- Polygamma functions -- Riemann zeta function.
505 0 $a Chapter 3. Other functions defined by integrals -- Introduction -- Error function and related functions -- Asymptotic series -- Fresnel integrals -- Applications -- Probability and statistics -- Heat conduction in solids -- Vibrating beams -- Exponential integral and related functions -- Logarithmic integral -- Sine and cosine integrals -- Elliptic integrals -- Limiting values and series representations -- The pendulum problem.
505 0 $a Chapter 4. Legendre polynomials and related functions -- Introduction -- Legendre polynomials -- The generating function -- Special values and recurrence formulas -- Legendre's differential equation -- Other representations of the legendre polynomials -- Rodrigues' formula -- Laplace integral formula -- Some bounds on Pn(x) -- Legendre series -- Orthogonality of the polynomials -- Finite legendre series -- Infinite legendre series -- Convergence of the series -- Piecewise continuous and piecewise smooth functions -- Pointwise convergence -- Legendre functions of the second kind -- Basic properties -- Associated legendre functions -- Basic properties of Pmn(x) -- Applications -- Electric potential due to a sphere -- Steady-state temperatures in a sphere.
505 0 $a Chapter 5. Other orthogonal polynomials -- Introduction -- Hermite polynomials -- Recurrence formulas -- Hermite series -- Simple harmonic oscillator -- Laguerre polynomials -- Recurrence formulas -- Laguerre series -- Associated laguerre polynomials -- The hydrogen atom -- Generalized polynomial sets -- Gegenbauer polynomials -- Chebyshev polynomials -- Jacobi polynomials.
505 0 $a Chapter 6. Bessel functions -- Introduction -- Bessel functions of the first kind -- The generating function -- Bessel functions of the nonintegral order -- Recurrence formulas -- Bessel's differential equation -- Integral representations -- Bessel's problem -- Geometric problems -- Integrals of Bessel functions -- Indefinite integrals -- Definite integrals -- Series involving Bessel functions -- Addition formulas -- Orthogonality of Bessel functions -- Fourier-Bessel series -- Bessel functions of the second kind -- Series expansion for Yn(x) -- Asymptotic formulas for small arguments -- Recurrence formulas -- Differential equations related to Bessel's equation -- The oscillating chain.
505 0 $a Chapter 7. Bessel functions of other kinds -- Introduction -- Modified Bessel functions -- Modified Bessel functions of the second kind -- Recurrence formulas -- Generating function and addition theorems -- Integral relations -- Integral representations -- Integrals of modified Bessel functions -- Spherical Bessel functions -- Recurrence formulas -- Modified spherical Bessel functions -- Other Bessel functions -- Hankel functions -- Struve functions -- Kelvin's functions -- Airy functions -- Asymptotic formulas -- Small arguments -- Large arguments.
505 0 $a Chapter 8. Applications involving Bessel functions -- Introduction -- Problems in mechanics -- The lengthening pendulum -- Buckling of a long column -- Statistical communication theory -- Narrowband noise and envelope detection -- Non-Rayleigh radar sea clutter -- Heat conduction and vibration phenomena -- Radial symmetric problems involving circles -- Radial symmetric problems involving cylinders -- The Helmholtz equation -- Step-index optical fibers -- Chapter 9. The hypergeometric function -- Introduction -- The Pochhammer symbol -- The function F(a,b;c;x) -- Elementary properties -- Integral representation -- The hypergeometric equation -- Relation to other functions -- Legendre functions -- Summing series and evaluating integrals -- Action-angle variables.
505 0 $a Chapter 10. The confluent hypergeometric functions -- Introduction -- The functions M(a;c;x) and U(a;c;x) -- Elementary properties of M(a;c;x) -- Confluent hypergeometric equation and U(a;c;x) -- Asymptotic formulas -- Relation to other functions -- Hermite functions -- Laguerre functions -- Whittaker functions -- Chapter 11. Generalized hypergeometric functions -- Introduction -- The set of functions pFq -- Hypergeometric-type series -- Other generalizations -- The Meijer G function -- The MacRobert E function -- Chapter 12. Applications involving hypergeometric-type functions -- Introduction -- Statistical communication theory -- Nonlinear devices -- Fluid mechanics -- Unsteady hydrodynamic flow past an infinite plate -- Transonic flow and the Euler-Tricomi equation -- Random fields -- Structure function of temperature -- Bibliography -- Appendix: A list of special function formulas -- Selected answers to exercises -- Index.
506 $a Restricted to subscribers or individual electronic text purchasers.
520 $a Modern engineering and physical science applications demand a thorough knowledge of applied mathematics, particularly special functions. These typically arise in applications such as communication systems, electro-optics, nonlinear wave propagation, electromagnetic theory, electric circuit theory, and quantum mechanics. This text systematically introduces special functions and explores their properties and applications in engineering and science.
530 $a Also available in print version.
538 $a System requirements: Adobe Acrobat Reader.
538 $a Mode of access: World Wide Web.
650 0 $a Functions, Special. $3 527750
710 2 $a Society of Photo-optical Instrumentation Engineers. $3 700253
830 0 $a SPIE Press monograph ; $v PM103. $3 877204
856 4 0 $u http://dx.doi.org/10.1117/3.270709