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Polynomial Sequences

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Polynomial Sequences

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Author : Francesco Aldo Costabile
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-12-18

Polynomial Sequences written by Francesco Aldo Costabile and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-18 with Mathematics categories.

Polynomials are useful mathematical tools. They are simply defined and can be calculated quickly on computer systems. They can be differentiated and integrated easily and can be pieced together to form spline curves. After Weierstrass approximation Theorem, polynomial sequences have acquired considerable importance not only in the various branches of Mathematics, but also in Physics, Chemistry and Engineering disciplines. There is a wide literature on specific polynomial sequences. But there is no literature that attempts a systematic exposition of the main basic methods for the study of a generic polynomial sequence and, at the same time, gives an overview of the main polynomial classes and related applications, at least in numerical analysis. In this book, through an elementary matrix calculus-based approach, an attempt is made to fill this gap by exposing dated and very recent results, both theoretical and applied.

On The Higher Order Sheffer Orthogonal Polynomial Sequences

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Author : Daniel J. Galiffa
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-04

On The Higher Order Sheffer Orthogonal Polynomial Sequences written by Daniel J. Galiffa 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 2013-01-04 with Mathematics categories.

On the Higher-Order Sheffer Orthogonal Polynomial Sequences sheds light on the existence/non-existence of B-Type 1 orthogonal polynomials. This book presents a template for analyzing potential orthogonal polynomial sequences including additional higher-order Sheffer classes. This text not only shows that there are no OPS for the special case the B-Type 1 class, but that there are no orthogonal polynomial sequences for the general B-Type 1 class as well. Moreover, it is quite provocative how the seemingly subtle transition from the B-Type 0 class to the B-Type 1 class leads to a drastically more difficult characterization problem. Despite this issue, a procedure is established that yields a definite answer to our current characterization problem, which can also be extended to various other characterization problems as well. Accessible to undergraduate students in the mathematical sciences and related fields, This book functions as an important reference work regarding the Sheffer sequences. The author takes advantage of Mathematica 7 to display unique detailed code and increase the reader's understanding of the implementation of Mathematica 7 and facilitate further experimentation. In addition, this book provides an excellent example of how packages like Mathematica 7 can be used to derive rigorous mathematical results.

Uniform Distribution Of Sequences Of Integers In Residue Classes

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Author : W. Narkiewicz
language : en
Publisher: Springer
Release Date : 2006-12-08

Uniform Distribution Of Sequences Of Integers In Residue Classes written by W. Narkiewicz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.

The Combinatorics Of Polynomial Sequences

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Author : David Lawrence Reiner
language : en
Publisher:
Release Date : 1975

The Combinatorics Of Polynomial Sequences written by David Lawrence Reiner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.

Elements Of Higher Mathematics

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Author : Frans Keune
language : en
Publisher: Radboud University Press
Release Date : 2024-10-29

Elements Of Higher Mathematics written by Frans Keune and has been published by Radboud University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-29 with Mathematics categories.

This is a textbook for beginning mathematics students. Knowledge of school mathematics is not presumed: it starts with the basics of counting. The underlying idea is that the best way to learn mathematics is by doing mathematics. For beginning students it is sometimes a problem to assume when looking for proof. For the exercises in this textbook, this situation does not occur: except for the introductory part all is built on Peano's axioms for the natural numbers, using the language of set theory only. The book starts explaining the way mathematics works: the use of intuitive set theory and the relation between language and mathematical entities. The common thread in the book is the construction of the number system all the way from the natural numbers, via the rationals and the reals to the complex numbers. For the student, the advantages of this approach are: - One learns concepts which are fundamental for all of mathematics. - The common thread offers a natural way for the introduction of these concepts. It helps to stay motivated during the course. - One learns to think like a mathematician. - One obtains insight into the way mathematics is built from simple ideas. - It helps to decide whether one is fitted for a mathematics study. For the interested reader also the other possible completions of the rationals - the p-adic numbers - are constructed. The book contains more than just the construction of the number system: there is also attention for its use, especially in combinatorics, number theory and cryptography, leaving mathematical analysis to the many textbooks for analysis and calculus courses.

Nilpotent Structures In Ergodic Theory

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Author : Bernard Host
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-12-12

Nilpotent Structures In Ergodic Theory written by Bernard Host 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 2018-12-12 with Mathematics categories.

Nilsystems play a key role in the structure theory of measure preserving systems, arising as the natural objects that describe the behavior of multiple ergodic averages. This book is a comprehensive treatment of their role in ergodic theory, covering development of the abstract theory leading to the structural statements, applications of these results, and connections to other fields. Starting with a summary of the relevant dynamical background, the book methodically develops the theory of cubic structures that give rise to nilpotent groups and reviews results on nilsystems and their properties that are scattered throughout the literature. These basic ingredients lay the groundwork for the ergodic structure theorems, and the book includes numerous formulations of these deep results, along with detailed proofs. The structure theorems have many applications, both in ergodic theory and in related fields; the book develops the connections to topological dynamics, combinatorics, and number theory, including an overview of the role of nilsystems in each of these areas. The final section is devoted to applications of the structure theory, covering numerous convergence and recurrence results. The book is aimed at graduate students and researchers in ergodic theory, along with those who work in the related areas of arithmetic combinatorics, harmonic analysis, and number theory.

Computer Mathematics Proceedings Of The Fifth Asian Symposium Ascm 2001

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Author : Kiyoshi Shirayanagi
language : en
Publisher: World Scientific
Release Date : 2001-09-18

Computer Mathematics Proceedings Of The Fifth Asian Symposium Ascm 2001 written by Kiyoshi Shirayanagi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-09-18 with Mathematics categories.

This volume covers some of the most recent and significant advances in computer mathematics, including algebraic, symbolic, numeric and geometric computation, automated mathematical reasoning, mathematical software and computer-aided geometric design. Researchers, engineers, academics and graduate students interested in doing mathematics using computers will find this volume good reading and a valuable reference.

Computer Mathematics

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Author : Kiyoshi Shirayanagi
language : en
Publisher: World Scientific
Release Date : 2001

Computer Mathematics written by Kiyoshi Shirayanagi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Computers categories.

A First Course On Orthogonal Polynomials

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Author : Kenier Castillo
language : en
Publisher: CRC Press
Release Date : 2024-11-19

A First Course On Orthogonal Polynomials written by Kenier Castillo and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-19 with Mathematics categories.

A First Course on Orthogonal Polynomials: Classical Orthogonal Polynomials and Related Topics provides an introduction to orthogonal polynomials and special functions aimed at graduate students studying these topics for the first time. A large part of its content is essentially inspired by the works of Pascal Maroni on the so-called algebraic theory of orthogonal polynomials, which distinguishes it from other contributions in the field. Features Suitable for a graduate course in orthogonal polynomials Can be used for a short course on the algebraic theory of orthogonal polynomials and its applicability to the study of the “old” classical orthogonal polynomials Includes numerous exercises for each topic Real and complex analysis are the only prerequisites

The Concrete Tetrahedron

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Author : Manuel Kauers
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-15

The Concrete Tetrahedron written by Manuel Kauers 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 2011-01-15 with Mathematics categories.

The book treats four mathematical concepts which play a fundamental role in many different areas of mathematics: symbolic sums, recurrence (difference) equations, generating functions, and asymptotic estimates. Their key features, in isolation or in combination, their mastery by paper and pencil or by computer programs, and their applications to problems in pure mathematics or to "real world problems" (e.g. the analysis of algorithms) are studied. The book is intended as an algorithmic supplement to the bestselling "Concrete Mathematics" by Graham, Knuth and Patashnik.

Polynomial Sequences

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