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• catalog abstract "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.".
• catalog contributor b10802392.
• catalog created "1998.".
• catalog date "1998".
• catalog date "1998.".
• catalog dateCopyrighted "1998.".
• catalog description "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.".
• catalog description "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.".
• catalog description "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.".
• catalog description "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.".
• catalog description "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.".
• catalog description "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.".
• catalog description "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.".
• catalog description "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.".
• catalog description "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.".
• catalog description "Includes bibliographical references (p. 451) and index.".
• catalog description "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.".
• catalog extent "xvii, 479 p. :".
• catalog identifier "0198565585 (OUP : hardcover)".
• catalog identifier "0819426164 (SPIE : hardcover)".
• catalog isPartOf "SPIE Press monograph ; PM49".
• catalog isPartOf "SPIE monograph ; 49.".
• catalog issued "1998".
• catalog issued "1998.".
• catalog language "eng".
• catalog publisher "Bellingham, Wash., USA : SPIE Optical Engineering Press ; Oxford : Oxford University Press,".
• catalog subject "515/.5 21".
• catalog subject "Functions, Special.".
• catalog subject "QA351 .A75 1998".
• catalog tableOfContents "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.".
• catalog tableOfContents "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.".
• catalog tableOfContents "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.".
• catalog tableOfContents "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.".
• catalog tableOfContents "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.".
• catalog tableOfContents "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.".
• catalog tableOfContents "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.".
• catalog tableOfContents "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.".
• catalog tableOfContents "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.".
• catalog title "Special functions of mathematics for engineers / Larry C. Andrews.".
• catalog type "text".