Introduction to real orthogonal polynomials
Thomas, William Howard, II
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The fundamental concept of orthogonality of mathematical objects occurs in a wide variety of physical and engineering disciplines. The theory of orthogonal functions, for example, is central to the development of Fourier series and wavelets, essential for signal processing. In particular, various families of classical orthogonal polynomials have traditionally been applied to fields such as electrostatics, numerical analysis, and many others. This thesis develops the main ideas necessary for understanding the classical theory of orthogonal polynomials. Special emphasis is given to the Jacobi polynomials and to certain important subclasses and generalizations, some recently discovered. Using the theory of hypergeometric power series and their q -extensions, various structural properties and relations between these classes are systematically investigated. Recently, these classes have found significant applications in coding theory and the study of angular momentum, and hold much promise for future applications.
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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