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ISBN: 9789814704038 9789814704045 9814704040 9814704032 Year: 2016 Publisher: New Jersey : World Scientific,
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"This book defines sets of orthogonal polynomials and derives a number of properties satisfied by any such set. It continues by describing the classical orthogonal polynomials and the additional properties they have. The first chapter defines the orthogonality condition for two functions. It then gives an iterative process to produce a set of polynomials which are orthogonal to one another and then describes a number of properties satisfied by any set of orthogonal polynomials. The classical orthogonal polynomials arise when the weight function in the orthogonality condition has a particular form. These polynomials have a further set of properties and in particular satisfy a second order differential equation. Each subsequent chapter investigates the properties of a particular polynomial set starting from its differential equation."--
Orthogonal polynomials. --- Polynomials. --- Polynômes orthogonaux --- Polynômes --- Algebra --- Fourier analysis --- Functions, Orthogonal --- Polynomials
ISBN: 9780521143479 9780521782012 0521782015 9781107325982 9781107095755 1107095751 9781107089457 110708945X 1107325986 0521143470 1139882813 1107103827 1107101336 9781139882811 9781107103825 9781107101333 Year: 2005 Volume: 98 Publisher: Cambridge ; New York : Cambridge University Press,
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The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback. Its encyclopedic coverage includes classical topics such as Jacobi, Hermite, Laguerre, Hahn, Charlier and Meixner polynomials as well as those discovered over the last 50 years, e.g. Askey-Wilson and Al-Salam-Chihara polynomial systems. Multiple orthogonal polynomials are discussed here for the first time in book form. Many modern applications of the subject are dealt with, including birth and death processes, integrable systems, combinatorics, and physical models. A chapter on open research problems and conjectures is designed to stimulate further research on the subject. Thoroughly updated and corrected since its original printing, this book continues to be valued as an authoritative reference not only by mathematicians, but also a wide range of scientists and engineers. Exercises ranging in difficulty are included to help both the graduate student and the newcomer.
Orthogonal polynomials. --- Polynômes orthogonaux --- Polynômes orthogonaux --- Orthogonal polynomials --- 517.518.8 --- 517.58 --- 517.518.8 Approximation of functions by polynomials and their generalizations --- Approximation of functions by polynomials and their generalizations --- 517.58 Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- Fourier analysis --- Functions, Orthogonal --- Polynomials --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials
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