Orthogonal Polynomials And Continued Fractions

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Continued Fractions and Orthogonal Functions

Author : S. Clement Cooper
Publisher : CRC Press
ISBN 13 : 1000111059
Total Pages : 400 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Continued Fractions and Orthogonal Functions by : S. Clement Cooper

Download or read book Continued Fractions and Orthogonal Functions written by S. Clement Cooper and published by CRC Press. This book was released on 2020-12-17 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference - the proceedings of a research conference held in Loen, Norway - contains information on the analytic theory of continued fractions and their application to moment problems and orthogonal sequences of functions. Uniting the research efforts of many international experts, this volume: treats strong moment problems, orthogonal polynomials and Laurent polynomials; analyses sequences of linear fractional transformations; presents convergence results, including truncation error bounds; considers discrete distributions and limit functions arising from indeterminate moment problems; discusses Szego polynomials and their applications to frequency analysis; describes the quadrature formula arising from q-starlike functions; and covers continued fractional representations for functions related to the gamma function.;This resource is intended for mathematical and numerical analysts; applied mathematicians; physicists; chemists; engineers; and upper-level undergraduate and agraduate students in these disciplines.

Recurrence Relations, Continued Fractions and Orthogonal Polynomials

Author : Richard Askey
Publisher : American Mathematical Soc.
ISBN 13 : 0821823019
Total Pages : 124 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recurrence Relations, Continued Fractions and Orthogonal Polynomials by : Richard Askey

Download or read book Recurrence Relations, Continued Fractions and Orthogonal Polynomials written by Richard Askey and published by American Mathematical Soc.. This book was released on 1984 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: We address the question of recovering the distribution function of a set of orthogonal polynomials from the three term recurrence relation satisfied by the polynomials. We investigate four sets of orthogonal polynomials: the Al-Salam-Chihara polynomials, random walk polynomials and their [italic]q-analogue, and the case [italic]q = -1 of the associated continuous [italic]q-ultraspherical polynomials. For each polynomial set we obtain generating functions, derive explicit representations as ordinary or basic hypergeometric functions and determine their asymptotic behavior

Orthogonal Polynomials and Continued Fractions

Author : S. V. Khrushchev
Publisher :
ISBN 13 : 9781107101586
Total Pages : 478 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Orthogonal Polynomials and Continued Fractions by : S. V. Khrushchev

Download or read book Orthogonal Polynomials and Continued Fractions written by S. V. Khrushchev and published by . This book was released on 2008 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This new and exciting historical book tells how Euler introduced the idea of orthogonal polynomials and how he combined them with continued fractions, as well as how Brouncker's formula of 1655 can be derived from Euler's efforts in Special Functions and Orthogonal Polynomials. The most interesting applications of this work are discussed, including the great Markoff's Theorem on the Lagrange spectrum, Abel's Theorem on integration in finite terms, Chebyshev's Theory of Orthogonal Polynomials, and very recent advances in Orthogonal Polynomials on the unit circle. As continued fractions become more important again, in part due to their use in finding algorithms in approximation theory, this timely book revives the approach of Wallis, Brouncker and Euler and illustrates the continuing significance of their influence. A translation of Euler's famous paper 'Continued Fractions, Observation' is included as an Addendum."--Publisher's description.

Orthogonal Polynomials and Continued Fractions

Author : Sergey Khrushchev
Publisher :
ISBN 13 : 9781107095984
Total Pages : 496 pages
Book Rating : 4.0/5 (959 download)

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Book Synopsis Orthogonal Polynomials and Continued Fractions by : Sergey Khrushchev

Download or read book Orthogonal Polynomials and Continued Fractions written by Sergey Khrushchev and published by . This book was released on 2014-05-18 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Full account of Euler's work on continued fractions and orthogonal polynomials; illustrates the significance of his work on mathematics today.

Orthogonal Polynomials and Continued Fractions

Author : S. V. Khrushchev
Publisher : Cambridge University Press
ISBN 13 : 0521854199
Total Pages : 0 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Orthogonal Polynomials and Continued Fractions by : S. V. Khrushchev

Download or read book Orthogonal Polynomials and Continued Fractions written by S. V. Khrushchev and published by Cambridge University Press. This book was released on 2008-07-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Full account of Euler's work on continued fractions and orthogonal polynomials; illustrates the significance of his work on mathematics today.

An Introduction to Orthogonal Polynomials

Author : Theodore S Chihara
Publisher : Courier Corporation
ISBN 13 : 0486479293
Total Pages : 276 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis An Introduction to Orthogonal Polynomials by : Theodore S Chihara

Download or read book An Introduction to Orthogonal Polynomials written by Theodore S Chihara and published by Courier Corporation. This book was released on 2011-02-17 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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"--

Orthogonal Functions

Author : William Jones
Publisher : CRC Press
ISBN 13 : 100011712X
Total Pages : 437 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Orthogonal Functions by : William Jones

Download or read book Orthogonal Functions written by William Jones and published by CRC Press. This book was released on 2020-12-22 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Oulines an array of recent work on the analytic theory and potential applications of continued fractions, linear functionals, orthogonal functions, moment theory, and integral transforms. Describes links between continued fractions. Pade approximation, special functions, and Gaussian quadrature."

Continued Fractions and Signal Processing

Author : Tomas Sauer
Publisher : Springer Nature
ISBN 13 : 3030843602
Total Pages : 275 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Continued Fractions and Signal Processing by : Tomas Sauer

Download or read book Continued Fractions and Signal Processing written by Tomas Sauer and published by Springer Nature. This book was released on 2021-09-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Besides their well-known value in number theory, continued fractions are also a useful tool in modern numerical applications and computer science. The goal of the book is to revisit the almost forgotten classical theory and to contextualize it for contemporary numerical applications and signal processing, thus enabling students and scientist to apply classical mathematics on recent problems. The books tries to be mostly self-contained and to make the material accessible for all interested readers. This provides a new view from an applied perspective, combining the classical recursive techniques of continued fractions with orthogonal problems, moment problems, Prony’s problem of sparse recovery and the design of stable rational filters, which are all connected by continued fractions.

Handbook of Continued Fractions for Special Functions

Author : Annie A.M. Cuyt
Publisher : Springer Science & Business Media
ISBN 13 : 1402069499
Total Pages : 430 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Handbook of Continued Fractions for Special Functions by : Annie A.M. Cuyt

Download or read book Handbook of Continued Fractions for Special Functions written by Annie A.M. Cuyt and published by Springer Science & Business Media. This book was released on 2008-04-12 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions. Of the standard work on the subject, the Handbook of mathematical functions with formulas, graphs and mathematical tables edited by Milton Abramowitz and Irene Stegun, the American National Institute of Standards claims to have sold over 700 000 copies! But so far no project has been devoted to the systematic study of continued fraction representations for these functions. This handbook is the result of such an endeavour. We emphasise that only 10% of the continued fractions contained in this book, can also be found in the Abramowitz and Stegun project or at the Wolfram website!

Continued Fractions with Applications

Author : L. Lorentzen
Publisher : North Holland
ISBN 13 :
Total Pages : 634 pages
Book Rating : 4.3/5 (97 download)

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Book Synopsis Continued Fractions with Applications by : L. Lorentzen

Download or read book Continued Fractions with Applications written by L. Lorentzen and published by North Holland. This book was released on 1992-11-08 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at two kinds of readers: firstly, people working in or near mathematics, who are curious about continued fractions; and secondly, senior or graduate students who would like an extensive introduction to the analytic theory of continued fractions. The book contains several recent results and new angles of approach and thus should be of interest to researchers throughout the field. The first five chapters contain an introduction to the basic theory, while the last seven chapters present a variety of applications. Finally, an appendix presents a large number of special continued fraction expansions. This very readable book also contains many valuable examples and problems.

Lectures in Algebraic Combinatorics

Author : Adriano M. Garsia
Publisher : Springer
ISBN 13 : 9783030583729
Total Pages : 232 pages
Book Rating : 4.5/5 (837 download)

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Book Synopsis Lectures in Algebraic Combinatorics by : Adriano M. Garsia

Download or read book Lectures in Algebraic Combinatorics written by Adriano M. Garsia and published by Springer. This book was released on 2020-10-07 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Capturing Adriano Garsia's unique perspective on essential topics in algebraic combinatorics, this book consists of selected, classic notes on a number of topics based on lectures held at the University of California, San Diego over the past few decades. The topics presented share a common theme of describing interesting interplays between algebraic topics such as representation theory and elegant structures which are sometimes thought of as being outside the purview of classical combinatorics. The lectures reflect Garsia’s inimitable narrative style and his exceptional expository ability. The preface presents the historical viewpoint as well as Garsia's personal insights into the subject matter. The lectures then start with a clear treatment of Alfred Young's construction of the irreducible representations of the symmetric group, seminormal representations and Morphy elements. This is followed by an elegant application of SL(2) representations to algebraic combinatorics. The last two lectures are on heaps, continued fractions and orthogonal polynomials with applications, and finally there is an exposition on the theory of finite fields. The book is aimed at graduate students and researchers in the field.

An Introduction to Orthogonal Polynomials

Author : Theodore S Chihara
Publisher : Courier Corporation
ISBN 13 : 0486141411
Total Pages : 276 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis An Introduction to Orthogonal Polynomials by : Theodore S Chihara

Download or read book An Introduction to Orthogonal Polynomials written by Theodore S Chihara and published by Courier Corporation. This book was released on 2014-07-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assuming no further prerequisites than a first undergraduate course in real analysis, this concise introduction covers general elementary theory related to orthogonal polynomials. It includes necessary background material of the type not usually found in the standard mathematics curriculum. Suitable for advanced undergraduate and graduate courses, it is also appropriate for independent study. 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. Numerous examples and exercises, an extensive bibliography, and a table of recurrence formulas supplement the text.

Orthogonal Polynomials

Author : Gabor Szeg
Publisher : American Mathematical Soc.
ISBN 13 : 0821810235
Total Pages : 448 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Orthogonal Polynomials by : Gabor Szeg

Download or read book Orthogonal Polynomials written by Gabor Szeg and published by American Mathematical Soc.. This book was released on 1939-12-31 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Analysis

Author : L. A. Lyusternik
Publisher : Elsevier
ISBN 13 : 1483194361
Total Pages : 419 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Mathematical Analysis by : L. A. Lyusternik

Download or read book Mathematical Analysis written by L. A. Lyusternik and published by Elsevier. This book was released on 2014-07-15 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Analysis: Functions, Limits, Series, Continued Fractions provides an introduction to the differential and integral calculus. This book presents the general problems of the theory of continuous functions of one and several variables, as well as the theory of limiting values for sequences of numbers and vectors. Organized into six chapters, this book begins with an overview of real numbers, the arithmetic linear continuum, limiting values, and functions of one variable. This text then presents the theory of series and practical methods of summation. Other chapters consider the theory of numerical series and series of functions and other analogous processes, particularly infinite continued fractions. This book discusses as well the general problems of the reduction of functions to orthogonal series. The final chapter deals with constants and the most important systems of numbers, including Bernoulli and Euler numbers. This book is a valuable resource for mathematicians, engineers, and research workers.

Orthogonal Polynomials

Author : Paul Nevai
Publisher : Springer Science & Business Media
ISBN 13 : 9400905017
Total Pages : 472 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Orthogonal Polynomials by : Paul Nevai

Download or read book Orthogonal Polynomials written by Paul Nevai and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the Proceedings of the NATO Advanced Study Institute on "Orthogonal Polynomials and Their Applications" held at The Ohio State University in Columbus, Ohio, U.S.A. between May 22,1989 and June 3,1989. The Advanced Study Institute primarily concentrated on those aspects of the theory and practice of orthogonal polynomials which surfaced in the past decade when the theory of orthogonal polynomials started to experience an unparalleled growth. This progress started with Richard Askey's Regional Confer ence Lectures on "Orthogonal Polynomials and Special Functions" in 1975, and subsequent discoveries led to a substantial revaluation of one's perceptions as to the nature of orthogonal polynomials and their applicability. The recent popularity of orthogonal polynomials is only partially due to Louis de Branges's solution of the Bieberbach conjecture which uses an inequality of Askey and Gasper on Jacobi polynomials. The main reason lies in their wide applicability in areas such as Pade approximations, continued fractions, Tauberian theorems, numerical analysis, probability theory, mathematical statistics, scattering theory, nuclear physics, solid state physics, digital signal processing, electrical engineering, theoretical chemistry and so forth. This was emphasized and convincingly demonstrated during the presentations by both the principal speakers and the invited special lecturers. The main subjects of our Advanced Study Institute included complex orthogonal polynomials, signal processing, the recursion method, combinatorial interpretations of orthogonal polynomials, computational problems, potential theory, Pade approximations, Julia sets, special functions, quantum groups, weighted approximations, orthogonal polynomials associated with root systems, matrix orthogonal polynomials, operator theory and group representations.

History of Continued Fractions and Padé Approximants

Author : Claude Brezinski
Publisher : Springer Science & Business Media
ISBN 13 : 3642581692
Total Pages : 556 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis History of Continued Fractions and Padé Approximants by : Claude Brezinski

Download or read book History of Continued Fractions and Padé Approximants written by Claude Brezinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: The history of continued fractions is certainly one of the longest among those of mathematical concepts, since it begins with Euclid's algorithm for the great est common divisor at least three centuries B.C. As it is often the case and like Monsieur Jourdain in Moliere's "Ie bourgeois gentilhomme" (who was speak ing in prose though he did not know he was doing so), continued fractions were used for many centuries before their real discovery. The history of continued fractions and Pade approximants is also quite im portant, since they played a leading role in the development of some branches of mathematics. For example, they were the basis for the proof of the tran scendence of 11' in 1882, an open problem for more than two thousand years, and also for our modern spectral theory of operators. Actually they still are of great interest in many fields of pure and applied mathematics and in numerical analysis, where they provide computer approximations to special functions and are connected to some convergence acceleration methods. Con tinued fractions are also used in number theory, computer science, automata, electronics, etc ...

Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach

Author : Percy Deift
Publisher : American Mathematical Soc.
ISBN 13 : 0821826956
Total Pages : 273 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach by : Percy Deift

Download or read book Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach written by Percy Deift and published by American Mathematical Soc.. This book was released on 2000 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random n times n matrices exhibit universal behavior as n > infinity? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems. Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.