In this thesis, a fairly detailed survey on the q-classical orthogonal polynomials of the Hahn
class is presented. Such polynomials appear to be the bounded solutions of the so called qhypergeometric
difference equation having polynomial coefficients of degree at most two. The
central idea behind our study is to discuss in a unified sense the orthogonality of all possible
polynomial solutions of the q-hypergeometric difference equation by means of a qualitative
analysis of the relevant q-Pearson equation. To be more specific, a geometrical approach has
been used by taking into account every posssible rational form of the polynomial coefficients,
together with various relative positions of their zeros, in the q-Pearson equation to describe a
desired q-weight function on a suitable orthogonality interval. Therefore, our method differs
from the standard ones which are based on the Favard theorem and the three-term recurrence
relation.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/12612758/index.pdf |
| Date | 01 December 2010 |
| Creators | Sevinik Adiguzel, Rezan |
| Contributors | Taseli, Hasan |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | Ph.D. Thesis |
| Format | text/pdf |
| Rights | Access forbidden for 1 year |
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