Polynomial Sequences : : Basic Methods, Special Classes, and Computational Applications / / Francesco Aldo Costabile, Maria Italia Gualtieri, Anna Napoli.

• VerfasserIn: Costabile, Francesco Aldo,; Gualtieri, Maria Italia,; Napoli, Anna,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2023]; 2024
• Year of Publication: 2023
• Language: English
• Series: De Gruyter Studies in Mathematics , 96
• Physical Description: 1 online resource (XVIII, 508 p.)

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 variousbranches 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.

Table of Contents

Frontmatter -- Preface -- Contents -- Part I: Basic methods -- Introduction -- 0 Infinite lower triangular matrices and formal power series -- 1 Polynomial sequences: algebraic structure, recurrence and determinant form, operational methods -- 2 Symmetric polynomial sequences -- 3 Generating functions -- 4 Differential operator and Sheffer classification -- 5 The monomiality principle -- Part II: Special classes of polynomial sequences -- Introduction -- 6 Sheffer polynomial sequences -- 7 Orthogonal polynomial sequences -- 8 Lidstone and central factorial-type polynomial sequences -- 9 Bernstein basis -- 10 Bivariate special polynomials: hints -- Part III: Computational applications -- Introduction -- 11 Approximation theory by operators -- 12 Interpolation -- 13 Boundary value problems and polynomial sequences -- 14 Appell and Lidstone-type quadrature formulas -- Postface -- Bibliography -- Index