Continued Fractions And Orthogonal Functions
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| Author | : S. Clement Cooper |
| Publisher | : CRC Press |
| Total Pages | : 402 |
| Release | : 2020-12-17 |
| Genre | : Mathematics |
| ISBN | : 1000154149 |
Download Continued Fractions and Orthogonal Functions Book in PDF, Epub and Kindle
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.
| Author | : William Jones |
| Publisher | : CRC Press |
| Total Pages | : 442 |
| Release | : 2020-12-22 |
| Genre | : Mathematics |
| ISBN | : 1000153673 |
Download Orthogonal Functions Book in PDF, Epub and Kindle
"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."
| Author | : Annie A.M. Cuyt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 430 |
| Release | : 2008-04-12 |
| Genre | : Mathematics |
| ISBN | : 1402069499 |
Download Handbook of Continued Fractions for Special Functions Book in PDF, Epub and Kindle
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!
| Author | : Richard Askey |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 124 |
| Release | : 1984 |
| Genre | : Mathematics |
| ISBN | : 0821823019 |
Download Recurrence Relations, Continued Fractions and Orthogonal Polynomials Book in PDF, Epub and Kindle
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
| Author | : S. Clement Cooper |
| Publisher | : CRC Press |
| Total Pages | : 400 |
| Release | : 2020-12-17 |
| Genre | : Mathematics |
| ISBN | : 1000111059 |
Download Continued Fractions and Orthogonal Functions Book in PDF, Epub and Kindle
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.
| Author | : L. A. Lyusternik |
| Publisher | : Elsevier |
| Total Pages | : 419 |
| Release | : 2014-07-15 |
| Genre | : Mathematics |
| ISBN | : 1483194361 |
Download Mathematical Analysis Book in PDF, Epub and Kindle
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.
| Author | : S. V. Khrushchev |
| Publisher | : |
| Total Pages | : 478 |
| Release | : 2008 |
| Genre | : Continued fractions |
| ISBN | : 9781107101586 |
Download Orthogonal Polynomials and Continued Fractions Book in PDF, Epub and Kindle
"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.
| Author | : S. V. Khrushchev |
| Publisher | : |
| Total Pages | : 478 |
| Release | : 2008 |
| Genre | : Continued fractions |
| ISBN | : 9781139883269 |
Download Orthogonal Polynomials and Continued Fractions Book in PDF, Epub and Kindle
"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.
| Author | : Claude Brezinski |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 556 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642581692 |
Download History of Continued Fractions and Padé Approximants Book in PDF, Epub and Kindle
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 ...
| Author | : Hubert Stanley Wall |
| Publisher | : Courier Dover Publications |
| Total Pages | : 449 |
| Release | : 2018-05-16 |
| Genre | : Mathematics |
| ISBN | : 0486830446 |
Download Analytic Theory of Continued Fractions Book in PDF, Epub and Kindle
One of the most authoritative and comprehensive books on the subject of continued fractions, this monograph has been widely used by generations of mathematicians and their students. Dr. Hubert Stanley Wall presents a unified theory correlating certain parts and applications of the subject within a larger analytic structure. Prerequisites include a first course in function theory and knowledge of the elementary properties of linear transformations in the complex plane. Some background in number theory, real analysis, and complex analysis may also prove helpful. The two-part treatment begins with an exploration of convergence theory, addressing continued fractions as products of linear fractional transformations, convergence theorems, and the theory of positive definite continued fractions, as well as other topics. The second part, focusing on function theory, covers the theory of equations, matrix theory of continued fractions, bounded analytic functions, and many additional subjects.
