On the Orthogonality of q-Classical Polynomials of the Hahn Class
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, cilt.8, 2012 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 8
- Basım Tarihi: 2012
- Doi Numarası: 10.3842/sigma.2012.042
- Dergi Adı: SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
The central idea behind this review article is to discuss in a unified sense the orthogonality of all possible polynomial solutions of the q-hypergeometric difference equation on a q-linear lattice by means of a qualitative analysis of the q-Pearson equation. To be more specific, a geometrical approach has been used by taking into account every possible rational form of the polynomial coefficients in the q-Pearson equation, together with various relative positions of their zeros, to describe a desired q-weight function supported on a suitable set of points. Therefore, our method differs from the standard ones which are based on the Favard theorem, the three-term recurrence relation and the difference equation of hypergeometric type. Our approach enables us to extend the orthogonality relations for some well-known q-polynomials of the Hahn class to a larger set of their parameters.