On The Higher Order Sheffer Orthogonal Polynomial Sequences

Download On The Higher Order Sheffer Orthogonal Polynomial Sequences full books in PDF, epub, and Kindle. Read online On The Higher Order Sheffer Orthogonal Polynomial Sequences ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

On the Higher-Order Sheffer Orthogonal Polynomial Sequences

Author : Daniel J. Galiffa
Publisher : Springer Science & Business Media
ISBN 13 : 1461459699
Total Pages : 118 pages
Book Rating : 4.4/5 (614 download)

DOWNLOAD NOW!

Book Synopsis On the Higher-Order Sheffer Orthogonal Polynomial Sequences by : Daniel J. Galiffa

Download or read book On the Higher-Order Sheffer Orthogonal Polynomial Sequences written by Daniel J. Galiffa and published by Springer Science & Business Media. This book was released on 2013-01-04 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

On the Higher-Order Sheffer Orthogonal Polynomial Sequences

Author : Springer
Publisher :
ISBN 13 : 9781461459705
Total Pages : 120 pages
Book Rating : 4.4/5 (597 download)

DOWNLOAD NOW!

Book Synopsis On the Higher-Order Sheffer Orthogonal Polynomial Sequences by : Springer

Download or read book On the Higher-Order Sheffer Orthogonal Polynomial Sequences written by Springer and published by . This book was released on 2013 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Polynomial Sequences

Author : Francesco Aldo Costabile
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311075732X
Total Pages : 598 pages
Book Rating : 4.1/5 (17 download)

DOWNLOAD NOW!

Book Synopsis Polynomial Sequences by : Francesco Aldo Costabile

Download or read book Polynomial Sequences written by Francesco Aldo Costabile and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-12-18 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Sheffer B-Type 1 Orthogonal Polynomial Sequences

Author : Daniel Joseph Galiffa
Publisher :
ISBN 13 :
Total Pages : 106 pages
Book Rating : 4.:/5 (53 download)

DOWNLOAD NOW!

Book Synopsis The Sheffer B-Type 1 Orthogonal Polynomial Sequences by : Daniel Joseph Galiffa

Download or read book The Sheffer B-Type 1 Orthogonal Polynomial Sequences written by Daniel Joseph Galiffa and published by . This book was released on 2009 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1939, I.M. Sheffer proved that every polynomial sequence belongs to one and only one type. Sheffer extensively developed properties of the B-Type 0 polynomial sequences and determined which sets are also orthogonal. He subsequently generalized his classification method to the case of arbitrary B-Type k by constructing the generalized generating function A(t)exp[xH1(t)+ ... + x[superscript k +1]H[subscript k](t)] = [summation sign] [infinity sign above summation sign] [subscript n=0 below summation sign]P[subscript n](x)t[superscript n], with H[subscript i](t) = h[subscript i], [subscript i]t[superscript i] + h[subscript i], [subscript i+1]t[superscript i+1] + ..., h1, 1 [does not equal] 0. Although extensive research has been done on characterizing polynomial sequences, no analysis has yet been completed on sets of type one or higher (k [greater than or equal to] 1). We present a preliminary analysis of a special case of the B-Type 1 (k = 1) class, which is an extension of the B-Type 0 class, in order to determine which sets, if any, are also orthogonal sets. Lastly, we consider an extension of this research and comment on future considerations. In this work the utilization of computer algebra packages is indispensable, as computational difficulties arise in the B-Type 1 class that are unlike those in the B-Type 0 class.

Modern Umbral Calculus

Author : Francesco Aldo Costabile
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110650096
Total Pages : 275 pages
Book Rating : 4.1/5 (16 download)

DOWNLOAD NOW!

Book Synopsis Modern Umbral Calculus by : Francesco Aldo Costabile

Download or read book Modern Umbral Calculus written by Francesco Aldo Costabile and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-06-17 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a novel approach to umbral calculus, which uses only elementary linear algebra (matrix calculus) based on the observation that there is an isomorphism between Sheffer polynomials and Riordan matrices, and that Sheffer polynomials can be expressed in terms of determinants. Additionally, applications to linear interpolation and operator approximation theory are presented in many settings related to various families of polynomials.

Theory, Methods and Applications of the Classical Hypergeometric Orthogonal Polynomial Sequences of Sheffer and Jacobi

Author : Dylan Jacob Langharst
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (18 download)

DOWNLOAD NOW!

Book Synopsis Theory, Methods and Applications of the Classical Hypergeometric Orthogonal Polynomial Sequences of Sheffer and Jacobi by : Dylan Jacob Langharst

Download or read book Theory, Methods and Applications of the Classical Hypergeometric Orthogonal Polynomial Sequences of Sheffer and Jacobi written by Dylan Jacob Langharst and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this Schreyer Honors Thesis is to explore theories, methods and applications oforthogonal polynomial sequences. This thesis is designed to be approachable and understandableby any undergraduate mathematics or physics major at The Pennsylvania State University in orderto serve as a learning resource. This paper is to be comprehensive and self-consistent; that is, wehope to cover all prerequisite information here that is required for the understanding of this paper,hence the thorough introduction. Throughout this paper, several definitions, terminologies andnotations are used, as listed in Chapter 1. The presentation of polynomial sequences here closelyfollow that in [1] and [2]. Limit, series and integral relations involving orthogonal polynomialsare presented in Chapter 2. Chapter 3 covers the inverse method and Schrdinger form for variousorthogonal polynomial sequences. Chapter 4 introduces applications of orthogonal polynomials inphysics and numerical analysis.

Orthogonal Polynomials

Author : Mama Foupouagnigni
Publisher : Springer Nature
ISBN 13 : 3030367444
Total Pages : 683 pages
Book Rating : 4.0/5 (33 download)

DOWNLOAD NOW!

Book Synopsis Orthogonal Polynomials by : Mama Foupouagnigni

Download or read book Orthogonal Polynomials written by Mama Foupouagnigni and published by Springer Nature. This book was released on 2020-03-11 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents contributions of international and local experts from the African Institute for Mathematical Sciences (AIMS-Cameroon) and also from other local universities in the domain of orthogonal polynomials and applications. The topics addressed range from univariate to multivariate orthogonal polynomials, from multiple orthogonal polynomials and random matrices to orthogonal polynomials and Painlevé equations. The contributions are based on lectures given at the AIMS-Volkswagen Stiftung Workshop on Introduction of Orthogonal Polynomials and Applications held on October 5–12, 2018 in Douala, Cameroon. This workshop, funded within the framework of the Volkswagen Foundation Initiative "Symposia and Summer Schools", was aimed globally at promoting capacity building in terms of research and training in orthogonal polynomials and applications, discussions and development of new ideas as well as development and enhancement of networking including south-south cooperation.

Orthogonal Polynomials and their Applications

Author : Manuel Alfaro
Publisher : Springer
ISBN 13 : 3540392955
Total Pages : 351 pages
Book Rating : 4.5/5 (43 download)

DOWNLOAD NOW!

Book Synopsis Orthogonal Polynomials and their Applications by : Manuel Alfaro

Download or read book Orthogonal Polynomials and their Applications written by Manuel Alfaro and published by Springer. This book was released on 2006-11-14 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Segovia meeting set out to stimulate an intensive exchange of ideas between experts in the area of orthogonal polynomials and its applications, to present recent research results and to reinforce the scientific and human relations among the increasingly international community working in orthogonal polynomials. This volume contains original research papers as well as survey papers about fundamental questions in the field (Nevai, Rakhmanov & López) and its relationship with other fields such as group theory (Koornwinder), Padé approximation (Brezinski), differential equations (Krall, Littlejohn) and numerical methods (Rivlin).

Combinatorics: The Rota Way

Author : Joseph P. S. Kung
Publisher : Cambridge University Press
ISBN 13 : 1139476769
Total Pages : 397 pages
Book Rating : 4.1/5 (394 download)

DOWNLOAD NOW!

Book Synopsis Combinatorics: The Rota Way by : Joseph P. S. Kung

Download or read book Combinatorics: The Rota Way written by Joseph P. S. Kung and published by Cambridge University Press. This book was released on 2009-02-09 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. His work on the foundations of combinatorics focused on the algebraic structures that lie behind diverse combinatorial areas, and created a new area of algebraic combinatorics. Written by two of his former students, this book is based on notes from his influential graduate courses and on face-to-face discussions. Topics include sets and valuations, partially ordered sets, distributive lattices, partitions and entropy, matching theory, free matrices, doubly stochastic matrices, Moebius functions, chains and antichains, Sperner theory, commuting equivalence relations and linear lattices, modular and geometric lattices, valuation rings, generating functions, umbral calculus, symmetric functions, Baxter algebras, unimodality of sequences, and location of zeros of polynomials. Many exercises and research problems are included, and unexplored areas of possible research are discussed. A must-have for all students and researchers in combinatorics and related areas.

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)

DOWNLOAD NOW!

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.

Differential Algebra, Complex Analysis and Orthogonal Polynomials

Author : Primitivo B. Acosta Humanez
Publisher : American Mathematical Soc.
ISBN 13 : 0821848860
Total Pages : 241 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!

Book Synopsis Differential Algebra, Complex Analysis and Orthogonal Polynomials by : Primitivo B. Acosta Humanez

Download or read book Differential Algebra, Complex Analysis and Orthogonal Polynomials written by Primitivo B. Acosta Humanez and published by American Mathematical Soc.. This book was released on 2010 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the 2007-2008 Jairo Charris Seminar in Algebra and Analysis on Differential Algebra, Complex Analysis and Orthogonal Polynomials, which was held at the Universidad Sergio Arboleda in Bogota, Colombia.

Methods for the Summation of Series

Author : Tian-Xiao He
Publisher : CRC Press
ISBN 13 : 1000534375
Total Pages : 301 pages
Book Rating : 4.0/5 (5 download)

DOWNLOAD NOW!

Book Synopsis Methods for the Summation of Series by : Tian-Xiao He

Download or read book Methods for the Summation of Series written by Tian-Xiao He and published by CRC Press. This book was released on 2022-01-26 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents methods for the summation of infinite and finite series and the related identities and inversion relations. The summation includes the column sums and row sums of lower triangular matrices. The convergence of the summation of infinite series is considered. The author’s focus is on symbolic methods and the Riordan array approach. In addition, this book contains hundreds summation formulas and identities, which can be used as a handbook for people working in computer science, applied mathematics, and computational mathematics, particularly, combinatorics, computational discrete mathematics, and computational number theory. The exercises at the end of each chapter help deepen understanding. Much of the materials in this book has never appeared before in textbook form. This book can be used as a suitable textbook for advanced courses for high lever undergraduate and lower lever graduate students. It is also an introductory self-study book for re- searchers interested in this field, while some materials of the book can be used as a portal for further research.

Encyclopedia of Statistical Sciences, Volume 12

Author :
Publisher : John Wiley & Sons
ISBN 13 : 0471744069
Total Pages : 562 pages
Book Rating : 4.4/5 (717 download)

DOWNLOAD NOW!

Book Synopsis Encyclopedia of Statistical Sciences, Volume 12 by :

Download or read book Encyclopedia of Statistical Sciences, Volume 12 written by and published by John Wiley & Sons. This book was released on 2005-12-16 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: ENCYCLOPEDIA OF STATISTICAL SCIENCES

The Umbral Calculus

Author : Steven Roman
Publisher : Courier Dover Publications
ISBN 13 : 0486839885
Total Pages : 209 pages
Book Rating : 4.4/5 (868 download)

DOWNLOAD NOW!

Book Synopsis The Umbral Calculus by : Steven Roman

Download or read book The Umbral Calculus written by Steven Roman and published by Courier Dover Publications. This book was released on 2019-04-17 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared toward upper-level undergraduates and graduate students, this elementary introduction to classical umbral calculus requires only an acquaintance with the basic notions of algebra and a bit of applied mathematics (such as differential equations) to help put the theory in mathematical perspective. The text focuses on classical umbral calculus, which dates back to the 1850s and continues to receive the attention of modern mathematicians. Subjects include Sheffer sequences and operators and their adjoints, with numerous examples of associated and other sequences. Related topics encompass the connection constants problem and duplication formulas, the Lagrange inversion formula, operational formulas, inverse relations, and binomial convolution. The final chapter offers a glimpse of the newer and less well-established forms of umbral calculus.

Orthogonal Polynomials

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

DOWNLOAD NOW!

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.

Orthogonal Polynomials

Author : Géza Freud
Publisher : Elsevier
ISBN 13 : 148315940X
Total Pages : 295 pages
Book Rating : 4.4/5 (831 download)

DOWNLOAD NOW!

Book Synopsis Orthogonal Polynomials by : Géza Freud

Download or read book Orthogonal Polynomials written by Géza Freud and published by Elsevier. This book was released on 2014-05-17 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orthogonal Polynomials contains an up-to-date survey of the general theory of orthogonal polynomials. It deals with the problem of polynomials and reveals that the sequence of these polynomials forms an orthogonal system with respect to a non-negative m-distribution defined on the real numerical axis. Comprised of five chapters, the book begins with the fundamental properties of orthogonal polynomials. After discussing the momentum problem, it then explains the quadrature procedure, the convergence theory, and G. Szego's theory. This book is useful for those who intend to use it as reference for future studies or as a textbook for lecture purposes

Laredo Lectures on Orthogonal Polynomials and Special Functions

Author : Renato Alvarez-Nodarse
Publisher : Nova Publishers
ISBN 13 : 9781594540097
Total Pages : 222 pages
Book Rating : 4.5/5 (4 download)

DOWNLOAD NOW!

Book Synopsis Laredo Lectures on Orthogonal Polynomials and Special Functions by : Renato Alvarez-Nodarse

Download or read book Laredo Lectures on Orthogonal Polynomials and Special Functions written by Renato Alvarez-Nodarse and published by Nova Publishers. This book was released on 2004 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book presents research in orthogonal polynomials and special functions. Recent developments in the theory and accomplishments of the last decade are pointed out and directions for research in the future are identified. The topics covered include matrix orthogonal polynomials, spectral theory and special functions, Asymptotics for orthogonal polynomials via Riemann-Hilbert methods, Polynomial wavelets and Koornwinder polynomials.