Title page for etd-0601115-121335


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URN etd-0601115-121335
Author Pei-kang Hsia
Author's Email Address No Public.
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Department Applied Mathematics
Year 2014
Semester 2
Degree Master
Type of Document
Language English
Title Some orthogonal polynomials and their general properties
Date of Defense 2015-05-27
Page Count 71
Keyword
  • Chebyshev polynomials
  • orthogonal polynomials
  • Laguerre polynomials
  • Jacobi polynomials
  • recur- rence relations and Favard’s Theorem
  • Abstract We shall study the mathematical properties of some classical orthogonal polynomials:
    Chebyshev polynomials of the first kind, Chebyshev polynomials of the second kind, Laguerre polynomials and Jacobi polynomials.
    All of these orthogonal polynomials observe the properties:
    (a)Rodrigues formula;
    (b)Orthogonal basis;
    (c)Associated differential equations;
    (d)Recurrence relations;
    (e)generating functions.
    These properties are the main reasons why these polynomials are important in mathematics and in applications.
    We shall study these properties for each of the above classical orthogonal polynomials in detail.
    On the other hand, we shall study the general relationship among these properties. Our work mainly follows the monographs of Folland and Chihara.
    Advisory Committee
  • Hsin-Yuan Huang - chair
  • Kung-Chien Wu - co-chair
  • Chun-Kong Law - advisor
  • Files
  • etd-0601115-121335.pdf
  • indicate access worldwide
    Date of Submission 2015-07-01

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