Title:
Special functions of mathematics for engineers / Larry C. Andrews.
SPIE Press monograph ;
SPIE monograph ;
Main Entry:
Andrews, Larry C.
Society of Photo-optical Instrumentation Engineers.
Publisher:
SPIE,
Publication Date:
1998.
Publication Place:
Bellingham, Wash. :
ISBN:
9780819478467
0819478466
9780198565581
0198565585
0819426164
9780819426161
Subject:
Functions, Special.
MATHEMATICS -- Calculus.
MATHEMATICS -- Mathematical Analysis.
Functions, Special.
Electronic books.
Series:
SPIE Press monograph ; PM49
SPIE monograph ; PM49.
Edition:
2nd ed.
Contents:
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.
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.
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.
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.
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.
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.
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.
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.
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.
Related Records:
Print version: Andrews, Larry C. Special functions of mathematics for engineers. 2nd ed. Bellingham, Wash. : SPIE, 1998 0819426164 (DLC) 97013896
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