Continued Fractions and Orthogonal Functions

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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.

Orthogonal Polynomials and Continued Fractions

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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

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Author :
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.

Recurrence Relations, Continued Fractions and Orthogonal Polynomials

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Author :
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 Functions

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Publisher : CRC Press
ISBN 13 : 1000153673
Total Pages : 442 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 442 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."

An Introduction to Orthogonal Polynomials

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Author :
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 Polynomials

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Author :
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.

Continued Fractions and Signal Processing

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Author :
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.

An Introduction to Orthogonal Polynomials

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Author :
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.

History of Continued Fractions and Padé Approximants

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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 ...

Mathematical Analysis

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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.

Continued Fractions

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821855720
Total Pages : 404 pages
Book Rating : 4.8/5 (557 download)

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Book Synopsis Continued Fractions by : Leo Jerome Lange

Download or read book Continued Fractions written by Leo Jerome Lange and published by American Mathematical Soc.. This book was released on 1999-07-28 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the contributions from the international conference held at the University of Missouri at Columbia, marking Professor Lange's 70th birthday and his retirement from the university. The principal purpose of the conference was to focus on continued fractions as a common interdisciplinary theme bridging gaps between a large number of fields--from pure mathematics to mathematical physics and approximation theory. Evident in this work is the widespread influence of continued fractions in a broad range of areas of mathematics and physics, including number theory, elliptic functions, Pade approximations, orthogonal polynomials, moment problems, frequency analysis, and regularity properties of evolution equations. Different areas of current research are represented. The lectures at the conference and the contributions to this volume reflect the wide range of applicability of continued fractions in mathematics and the applied sciences.

Orthogonal Polynomials

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Author :
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 Szegš

Download or read book Orthogonal Polynomials written by Gabor Szegš 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.

A Bibliography on Continued Fractions, Padé Approximation, Sequence Transformation and Related Subjects

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Publisher :
ISBN 13 :
Total Pages : 354 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis A Bibliography on Continued Fractions, Padé Approximation, Sequence Transformation and Related Subjects by : Claude Brezinski

Download or read book A Bibliography on Continued Fractions, Padé Approximation, Sequence Transformation and Related Subjects written by Claude Brezinski and published by . This book was released on 1991 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Continued Fractions and Padé Approximants

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Author :
Publisher : North Holland
ISBN 13 :
Total Pages : 354 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Continued Fractions and Padé Approximants by : Claude Brezinski

Download or read book Continued Fractions and Padé Approximants written by Claude Brezinski and published by North Holland. This book was released on 1990 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Padeacute; approximants and continued fractions are typical examples of old areas of mathematics (continued fractions can be traced back to Euclid's g.c.d. algorithm more than 2000 years ago) which are again very much alive. This is due to their numerous applications in number theory, cryptography, statistics, numerical analysis, special functions, digital filtering, signal processing, fractals, fluid mechanics, theoretical physics, chemistry, engineering etc. This renewal of interest is also due to their intimate connection with other important topics such as orthogonal polynomials (another old subject now again in full vitality), rational approximation, Gaussian quadratures, extrapolation and convergence acceleration methods, differential equations etc.

An Introduction to Orthogonal Polynomials

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Publisher :
ISBN 13 : 9781306937825
Total Pages : 249 pages
Book Rating : 4.9/5 (378 download)

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

Download or read book An Introduction to Orthogonal Polynomials written by Theodore Seio Chihara and published by . This book was released on 2014-01-01 with total page 249 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.

Communications in the Analytic Theory of Continued Fractions

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Author :
Publisher :
ISBN 13 :
Total Pages : 84 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Communications in the Analytic Theory of Continued Fractions by :

Download or read book Communications in the Analytic Theory of Continued Fractions written by and published by . This book was released on 2007 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: