On The Higher Order Sheffer Orthogonal Polynomial Sequences
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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.
On The Higher Order Sheffer Orthogonal Polynomial Sequences
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Author : Springer
language : en
Publisher:
Release Date : 2013
On The Higher Order Sheffer Orthogonal Polynomial Sequences written by Springer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
The Sheffer B Type 1 Orthogonal Polynomial Sequences
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Author : Daniel Joseph Galiffa
language : en
Publisher:
Release Date : 2009
The Sheffer B Type 1 Orthogonal Polynomial Sequences written by Daniel Joseph Galiffa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Generating functions categories.
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.
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.
Theory Methods And Applications Of The Classical Hypergeometric Orthogonal Polynomial Sequences Of Sheffer And Jacobi
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Author : Dylan Jacob Langharst
language : en
Publisher:
Release Date : 2018
Theory Methods And Applications Of The Classical Hypergeometric Orthogonal Polynomial Sequences Of Sheffer And Jacobi written by Dylan Jacob Langharst and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
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.
Modern Umbral Calculus
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Author : Francesco Aldo Costabile
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-06-17
Modern Umbral Calculus 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 2019-06-17 with Mathematics categories.
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.
An Introduction To Orthogonal Polynomials
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Author : Theodore S Chihara
language : en
Publisher: Courier Corporation
Release Date : 2014-07-01
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 2014-07-01 with Mathematics categories.
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.
Orthogonal Polynomials
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Author : Mama Foupouagnigni
language : en
Publisher: Springer Nature
Release Date : 2020-03-11
Orthogonal Polynomials written by Mama Foupouagnigni and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-11 with Mathematics categories.
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
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Author : Manuel Alfaro
language : en
Publisher: Springer
Release Date : 2006-11-14
Orthogonal Polynomials And Their Applications written by Manuel Alfaro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
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
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Author : Joseph P. S. Kung
language : en
Publisher: Cambridge University Press
Release Date : 2009-02-09
Combinatorics The Rota Way written by Joseph P. S. Kung and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-09 with Mathematics categories.
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.