Introduction to real orthogonal polynomials

Download
Author
Thomas, William Howard, II
Date
1992-06Advisor
Fischer, Ismor
Metadata
Show full item recordAbstract
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.
Rights
This 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.Collections
Related items
Showing items related by title, author, creator and subject.
-
Laser Propagation in Biaxial Liquid Crystal Polymers
Choate, Eric P.; Zhou, Hong (2011);We examine the propagation of a laser beam through a liquid crystal polymer (LCP) layer using the finite-difference time-domain (FDTD) method. Anchoring conditions on supporting glass plates induce an orientational ... -
Packing in two and three dimensions
Martins, Gustavo H. A. (2003-06);This dissertation investigates Multidimensional Packing Problems (MD-PPs): the Pallet Loading Problem (PLP), the Multidimensional Knapsack Problem (MD-KP), and the Multidimensional Bin Packing Problem (MD-BPP). In these ... -
Nonlinear Beam Kinematics by Decomposition of the Rotation Tensor
Danielson, D.A.; Hodges, D.H. (1987-06);A simple matrix expression is obtained for the strain components of a beam in which the displacements and rotations are large. The only restrictions are on the magnitudes of the strain and of the local rotation, a ...