Special functions of mathematics for engineers [electronic resource] / Larry C. Andrews.
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, a...
Saved in:
| Online Access: |
Full Text (via SPIE Digital Library) |
|---|---|
| Main Author: | |
| Corporate Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Bellingham, Wash. :
SPIE,
1998.
|
| Edition: | 2nd ed. |
| Subjects: |
MARC
| LEADER | 00000cam a2200000xa 4500 | ||
|---|---|---|---|
| 001 | b11042636 | ||
| 003 | CoU | ||
| 006 | m o d | ||
| 007 | cr ||||||||||| | ||
| 008 | 090906r19981992waua fob 001 0 eng d | ||
| 005 | 20230925220851.7 | ||
| 019 | |a 508394855 |a 1027372488 |a 1048758991 |a 1058094031 |a 1066677347 |a 1067097764 |a 1116919613 |a 1119422574 | ||
| 020 | |a 9780819478467 |q (electronic bk.) | ||
| 020 | |a 0819478466 |q (electronic bk.) | ||
| 020 | |z 9780198565581 | ||
| 020 | |z 0198565585 | ||
| 020 | |z 0819426164 |q (print) | ||
| 020 | |z 9780819426161 |q (print) | ||
| 024 | 7 | |a 10.1117/3.270709 | |
| 035 | |a (OCoLC)spie435971874 | ||
| 035 | |a (OCoLC)435971874 |z (OCoLC)508394855 |z (OCoLC)1027372488 |z (OCoLC)1048758991 |z (OCoLC)1058094031 |z (OCoLC)1066677347 |z (OCoLC)1067097764 |z (OCoLC)1116919613 |z (OCoLC)1119422574 | ||
| 040 | |a CaBNvSL |b eng |e pn |c J2I |d ZCU |d OCLCQ |d CEF |d SPIES |d EBLCP |d E7B |d OCLCO |d OCLCQ |d OCLCA |d OCLCF |d DEBSZ |d OCLCQ |d OCLCO |d OCLCQ |d N$T |d YDXCP |d OCLCQ |d COO |d MERUC |d BUF |d KIJ |d U3W |d OCLCA |d AU@ |d OCLCQ |d WYU |d UWO |d OCLCQ |d S2H |d OCLCQ | ||
| 049 | |a GWRE | ||
| 050 | 4 | |a QA351 |b .A75 1998e | |
| 100 | 1 | |a Andrews, Larry C. |0 http://id.loc.gov/authorities/names/n81131021 |1 http://isni.org/isni/0000000108946704. | |
| 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. : |b SPIE, |c 1998. | ||
| 300 | |a 1 online resource (xvii, 479 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent. | ||
| 337 | |a computer |b c |2 rdamedia. | ||
| 338 | |a online resource |b cr |2 rdacarrier. | ||
| 500 | |a "SPIE monograph PM49." | ||
| 500 | |a "SPIE digital library." | ||
| 500 | |a Copublished with Oxford University Press. | ||
| 500 | |a Originally published: 2nd edition New York : McGraw-Hill, ©1992. | ||
| 504 | |a Includes bibliographical references (page 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 | 8 | |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 | 8 | |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 | 8 | |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 | 8 | |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 | 8 | |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 | 8 | |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 | 8 | |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 | 8 | |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. | |
| 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. | ||
| 650 | 0 | |a Functions, Special. |0 http://id.loc.gov/authorities/subjects/sh85052348. | |
| 650 | 7 | |a Functions, Special. |2 fast |0 (OCoLC)fst00936132. | |
| 710 | 2 | |a Society of Photo-Optical Instrumentation Engineers. |0 http://id.loc.gov/authorities/names/n78088934 |1 http://isni.org/isni/0000000122965856. | |
| 776 | 0 | 8 | |i Print version: |a Andrews, Larry C. |t Special functions of mathematics for engineers. |b 2nd ed. |d Bellingham, Wash. : SPIE, 1998 |z 0819426164 |w (DLC) 97013896. |
| 856 | 4 | 0 | |u https://colorado.idm.oclc.org/login?url=https://doi.org/10.1117/3.270709 |z Full Text (via SPIE Digital Library) |
| 907 | |a .b110426368 |b 10-17-22 |c 06-11-20 | ||
| 915 | |a I | ||
| 998 | |a web |b 06-30-20 |c b |d b |e - |f eng |g wau |h 0 |i 1 | ||
| 907 | |a .b110426368 |b 06-30-20 |c 06-11-20 | ||
| 944 | |a MARS - RDA ENRICHED | ||
| 956 | |a SPIE eBooks | ||
| 956 | |b SPIE eBooks | ||
| 999 | f | f | |i 369489dd-ca6c-5304-a814-9c8282aa5985 |s e0f53288-d9fd-5d78-b0b4-60dcb67a2039 |
| 952 | f | f | |p Can circulate |a University of Colorado Boulder |b Online |c Online |d Online |e QA351 .A75 1998e |h Library of Congress classification |i web |n 1 |