On the q-analysis of q-hypergeometric difference equation

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2010
Sevindik-Adıgüzel, Rezan
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.

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Citation Formats
R. Sevindik-Adıgüzel, “On the q-analysis of q-hypergeometric difference equation,” Ph.D. - Doctoral Program, Middle East Technical University, 2010.