Orthogonal Polynomials

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 Content: Front Matter, Page iii Copyright, Page iv Preface, Pages 5-6 Notations, Page 9 CHAPTER I - Fundamental Properties of Orthogonal Polynomials, Pages 11-53 CHAPTER II - Elements of the Theory of the Hamburger–Stieltjes Momentum Problem, Pages 54-87 CHAPTER III - Quadrature Procedure and Interpolation over the Zeros of the Orthogonal Polynomials, Pages 88-137 CHAPTER IV - Convergence Theory of the Series of Orthogonal Polynomials, Pages 138-186 CHAPTER V - The Theory of G. Szegő, Pages 187-272 Some unsolved problems, Pages 273-277 Bibliography, Pages 279-290 Author index, Pages 291-292 Subject index, Pages 293-294