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.
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.
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.
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.
Polynomial Sequences And Their Applications
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Author : Francesco Aldo Costabile
language : en
Publisher:
Release Date : 2024-03-05
Polynomial Sequences And Their Applications written by Francesco Aldo Costabile and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-05 with Computers categories.
The present reprint contains the articles accepted and published in the Special Issue "Polynomial Sequences and Their Applications" of the MDPI journal Mathematics. This reprint aims to present, albeit partially, the state of the art on the theory and application of polynomial sequences. Polynomials are incredibly useful mathematical tools, as 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. Sequences of polynomials perform an important role in several branches of science, including mathematics, physics, and engineering. This volume contains both theoretical works and practical applications in the field of polynomial sequences and their applications.
Polynomial Sequences
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Author : Larry Johansson
language : en
Publisher:
Release Date : 1974
Polynomial Sequences written by Larry Johansson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Polynomials categories.
Elliptic Polynomials
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Author : J.S. Lomont
language : en
Publisher: CRC Press
Release Date : 2000-08-31
Elliptic Polynomials written by J.S. Lomont and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-08-31 with Mathematics categories.
A remarkable interplay exists between the fields of elliptic functions and orthogonal polynomials. In the first monograph to explore their connections, Elliptic Polynomials combines these two areas of study, leading to an interesting development of some basic aspects of each. It presents new material about various classes of polynomials and about t
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.
Unimodal Log Concave And Polya Frequency Sequences In Combinatorics
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Author : Francesco Brenti
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Unimodal Log Concave And Polya Frequency Sequences In Combinatorics written by Francesco Brenti 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 1989 with Combinatorial analysis categories.
Many sequences of combinatorial interest are known to be unimodal or log-concave and there has been a considerable amount of interest devoted to this topic. The main object of this work is to point out another branch of mathematics that can be successfully used to attack these kinds of problems, namely, the theory of total positivity.