Author: Herbert Stahl
Publisher: Cambridge University Press
ISBN: 9780521415347
Category : Mathematics
Languages : en
Pages : 272
Book Description
An encyclopedic presentation of general orthogonal polynomials, placing emphasis on asymptotic behaviour and zero distribution.
General Orthogonal Polynomials
Author: Herbert Stahl
Publisher: Cambridge University Press
ISBN: 9780521415347
Category : Mathematics
Languages : en
Pages : 272
Book Description
An encyclopedic presentation of general orthogonal polynomials, placing emphasis on asymptotic behaviour and zero distribution.
Publisher: Cambridge University Press
ISBN: 9780521415347
Category : Mathematics
Languages : en
Pages : 272
Book Description
An encyclopedic presentation of general orthogonal polynomials, placing emphasis on asymptotic behaviour and zero distribution.
Orthogonal Polynomials
Author: Gabor Szeg
Publisher: American Mathematical Soc.
ISBN: 0821810235
Category : Mathematics
Languages : en
Pages : 448
Book Description
The general theory of orthogonal polynomials was developed in the late 19th century from a study of continued fractions by P. L. Chebyshev, even though special cases were introduced earlier by Legendre, Hermite, Jacobi, Laguerre, and Chebyshev himself. It was further developed by A. A. Markov, T. J. Stieltjes, and many other mathematicians. The book by Szego, originally published in 1939, is the first monograph devoted to the theory of orthogonal polynomials and its applications in many areas, including analysis, differential equations, probability and mathematical physics. Even after all the years that have passed since the book first appeared, and with many other books on the subject published since then, this classic monograph by Szego remains an indispensable resource both as a textbook and as a reference book. It can be recommended to anyone who wants to be acquainted with this central topic of mathematical analysis.
Publisher: American Mathematical Soc.
ISBN: 0821810235
Category : Mathematics
Languages : en
Pages : 448
Book Description
The general theory of orthogonal polynomials was developed in the late 19th century from a study of continued fractions by P. L. Chebyshev, even though special cases were introduced earlier by Legendre, Hermite, Jacobi, Laguerre, and Chebyshev himself. It was further developed by A. A. Markov, T. J. Stieltjes, and many other mathematicians. The book by Szego, originally published in 1939, is the first monograph devoted to the theory of orthogonal polynomials and its applications in many areas, including analysis, differential equations, probability and mathematical physics. Even after all the years that have passed since the book first appeared, and with many other books on the subject published since then, this classic monograph by Szego remains an indispensable resource both as a textbook and as a reference book. It can be recommended to anyone who wants to be acquainted with this central topic of mathematical analysis.
An Introduction to Orthogonal Polynomials
Author: Theodore S Chihara
Publisher: Courier Corporation
ISBN: 0486479293
Category : Mathematics
Languages : en
Pages : 276
Book Description
"This concise introduction covers general elementary theory related to orthogonal polynomials and assumes only a first undergraduate course in real analysis. Topics include the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula and properties of orthogonal polynomials, special functions, and some specific systems of orthogonal polynomials. 1978 edition"--
Publisher: Courier Corporation
ISBN: 0486479293
Category : Mathematics
Languages : en
Pages : 276
Book Description
"This concise introduction covers general elementary theory related to orthogonal polynomials and assumes only a first undergraduate course in real analysis. Topics include the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula and properties of orthogonal polynomials, special functions, and some specific systems of orthogonal polynomials. 1978 edition"--
The Classical Orthogonal Polynomials
Author: Doman Brian George Spencer
Publisher: World Scientific
ISBN: 9814704059
Category : Mathematics
Languages : en
Pages : 176
Book Description
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.
Publisher: World Scientific
ISBN: 9814704059
Category : Mathematics
Languages : en
Pages : 176
Book Description
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.
Discrete Orthogonal Polynomials. (AM-164)
Author: J. Baik
Publisher: Princeton University Press
ISBN: 0691127344
Category : Mathematics
Languages : en
Pages : 178
Book Description
Publisher description
Publisher: Princeton University Press
ISBN: 0691127344
Category : Mathematics
Languages : en
Pages : 178
Book Description
Publisher description
Classical and Quantum Orthogonal Polynomials in One Variable
Author: Mourad Ismail
Publisher: Cambridge University Press
ISBN: 9780521782012
Category : Mathematics
Languages : en
Pages : 748
Book Description
The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.
Publisher: Cambridge University Press
ISBN: 9780521782012
Category : Mathematics
Languages : en
Pages : 748
Book Description
The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.
Orthogonal Polynomials of Several Variables
Author: Charles F. Dunkl
Publisher: Cambridge University Press
ISBN: 1107071895
Category : Mathematics
Languages : en
Pages : 439
Book Description
Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.
Publisher: Cambridge University Press
ISBN: 1107071895
Category : Mathematics
Languages : en
Pages : 439
Book Description
Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.
Padé-type approximation and general orthogonal polynomials
Orthogonal Polynomials
Author: Géza Freud
Publisher: Elsevier
ISBN: 148315940X
Category : Mathematics
Languages : en
Pages : 294
Book Description
Orthogonal Polynomials contains an up-to-date survey of the general theory of orthogonal polynomials. It deals with the problem of polynomials and reveals that the sequence of these polynomials forms an orthogonal system with respect to a non-negative m-distribution defined on the real numerical axis. Comprised of five chapters, the book begins with the fundamental properties of orthogonal polynomials. After discussing the momentum problem, it then explains the quadrature procedure, the convergence theory, and G. Szegő's theory. This book is useful for those who intend to use it as reference for future studies or as a textbook for lecture purposes
Publisher: Elsevier
ISBN: 148315940X
Category : Mathematics
Languages : en
Pages : 294
Book Description
Orthogonal Polynomials contains an up-to-date survey of the general theory of orthogonal polynomials. It deals with the problem of polynomials and reveals that the sequence of these polynomials forms an orthogonal system with respect to a non-negative m-distribution defined on the real numerical axis. Comprised of five chapters, the book begins with the fundamental properties of orthogonal polynomials. After discussing the momentum problem, it then explains the quadrature procedure, the convergence theory, and G. Szegő's theory. This book is useful for those who intend to use it as reference for future studies or as a textbook for lecture purposes
Fourier Series in Orthogonal Polynomials
Author: Boris Osilenker
Publisher: World Scientific
ISBN: 9789810237875
Category : Mathematics
Languages : en
Pages : 304
Book Description
This book presents a systematic coarse on general orthogonal polynomials and Fourie series in orthogonal polynomials. It consists of six chapters. Chapter 1 deals in essence with standard results from the university course on the function theory of a real variable and on functional analysis. Chapter 2 contains the classical results about the orthogonal polynomials (some properties, classical Jacobi polynomials and the criteria of boundedness). The main subject of the book is Fourier series in general orthogonal polynomials. Chapters 3 and 4 are devoted to some results in this topic (classical results about convergence and summability of Fourier series in L(2)micro; summability almost everywhere by the Cesaro means and the Poisson-Abel method for Fourier polynomial series are the subject of Chapters 4 and 5). The last chapter contains some estimates regarding the generalized shift operator and the generalized product formula, associated with general orthogonal polynomials. The starting point of the technique in Chapters 4 and 5 is the representations of bilinear and trilinear forms obtained by the author. The results obtained in these two chapters are new ones. Chapters 2 and 3 (and part of Chapter 1) will be useful to postgraduate students, and one can choose them for treatment. This book is intended for researchers (mathematicians and physicists) whose work involves function theory, functional analysis, harmonic analysis and approximation theory.
Publisher: World Scientific
ISBN: 9789810237875
Category : Mathematics
Languages : en
Pages : 304
Book Description
This book presents a systematic coarse on general orthogonal polynomials and Fourie series in orthogonal polynomials. It consists of six chapters. Chapter 1 deals in essence with standard results from the university course on the function theory of a real variable and on functional analysis. Chapter 2 contains the classical results about the orthogonal polynomials (some properties, classical Jacobi polynomials and the criteria of boundedness). The main subject of the book is Fourier series in general orthogonal polynomials. Chapters 3 and 4 are devoted to some results in this topic (classical results about convergence and summability of Fourier series in L(2)micro; summability almost everywhere by the Cesaro means and the Poisson-Abel method for Fourier polynomial series are the subject of Chapters 4 and 5). The last chapter contains some estimates regarding the generalized shift operator and the generalized product formula, associated with general orthogonal polynomials. The starting point of the technique in Chapters 4 and 5 is the representations of bilinear and trilinear forms obtained by the author. The results obtained in these two chapters are new ones. Chapters 2 and 3 (and part of Chapter 1) will be useful to postgraduate students, and one can choose them for treatment. This book is intended for researchers (mathematicians and physicists) whose work involves function theory, functional analysis, harmonic analysis and approximation theory.