Castillo K. A First Course on Orthogonal Polynomials...and Related Topics 2024

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Castillo K. A First Course on Orthogonal Polynomials...and Related Topics 2024

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Textbook in PDF format 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 analyses are the only prerequisites Dedication Preface Authors Symbol Description Foundations of the Algebraic Theory Orthogonal Polynomial Sequences Zeros and Gauss-Jacobi Mechanical Quadrature The Spectral Theorem The Markov Theorem Orthogonal Polynomials and Dual Basis Functional Differential Equation Classical Orthogonal Polynomials: General Properties Functional Equation on Lattices Classical Orthogonal Polynomials: The Positive Definite Case Hypergeometric Series Locally Convex Spaces Bibliography Index