Orthogonal Polynomials And Continued Fractions
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Orthogonal Polynomials And Continued Fractions
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Author : Sergey Khrushchev
language : en
Publisher:
Release Date : 2014-05-18
Orthogonal Polynomials And Continued Fractions written by Sergey Khrushchev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-18 with Continued fractions categories.
Full account of Euler's work on continued fractions and orthogonal polynomials; illustrates the significance of his work on mathematics today.
Continued Fractions And Orthogonal Functions
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Author : S. Clement Cooper
language : en
Publisher: CRC Press
Release Date : 2020-12-17
Continued Fractions And Orthogonal Functions written by S. Clement Cooper and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Mathematics categories.
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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Author : S. V. Khrushchev
language : en
Publisher:
Release Date : 2014-05-22
Orthogonal Polynomials And Continued Fractions written by S. V. Khrushchev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-22 with MATHEMATICS categories.
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 : S. V. Khrushchev
language : en
Publisher:
Release Date : 2008
Orthogonal Polynomials And Continued Fractions written by S. V. Khrushchev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Continued fractions categories.
"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.
Lectures In Algebraic Combinatorics
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Author : Adriano M. Garsia
language : en
Publisher: Springer Nature
Release Date : 2020-10-06
Lectures In Algebraic Combinatorics written by Adriano M. Garsia and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-06 with Mathematics categories.
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.
Recurrence Relations Continued Fractions And Orthogonal Polynomials
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Author : Richard Askey
language : en
Publisher: American Mathematical Soc.
Release Date : 1984
Recurrence Relations Continued Fractions And Orthogonal Polynomials written by Richard Askey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
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
Continued Fractions From Analytic Number Theory To Constructive Approximation
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Author : Bruce C. Berndt
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Continued Fractions From Analytic Number Theory To Constructive Approximation written by Bruce C. Berndt and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
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, Padé 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.
An Introduction To Orthogonal Polynomials
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Author : Theodore S Chihara
language : en
Publisher: Courier Corporation
Release Date : 2011-02-17
An Introduction To Orthogonal Polynomials written by Theodore S Chihara and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-17 with Mathematics categories.
"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"--
Handbook Of Continued Fractions For Special Functions
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Author : Annie A.M. Cuyt
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-12
Handbook Of Continued Fractions For Special Functions written by Annie A.M. Cuyt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-12 with Mathematics categories.
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!
Analytic Theory Of Continued Fractions
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Author : W. B. Jones
language : en
Publisher: Springer
Release Date : 2006-11-17
Analytic Theory Of Continued Fractions written by W. B. Jones and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-17 with Mathematics categories.