Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
On the q-analysis of q-hypergeometric difference equation
Download
index.pdf
Date
2010
Author
Sevindik-Adıgüzel, Rezan
Metadata
Show full item record
Item Usage Stats
69
views
38
downloads
Cite This
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.
Subject Keywords
Q-linear lattices.
,
Q-hypergeometric.
URI
http://etd.lib.metu.edu.tr/upload/12612758/index.pdf
https://hdl.handle.net/11511/20768
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
On the Orthogonality of q-Classical Polynomials of the Hahn Class
Alvarez-Nodarse, Renato; Adiguzel, Rezan Sevinik; Taşeli, Hasan (2012-01-01)
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-wei...
On the Interval Baker-Thompson Rule
Gok, S. Z. Alparslan (Hindawi Limited, 2012)
The main aim of this paper is to give an axiomatic characterization of the interval Baker-Thompson rule.
Pseudospectral methods for differential equations : application to the Schrödinger type eigenvalue problems
Alıcı, Haydar; Taşeli, Hasan; Department of Mathematics (2003)
In this thesis, a survey on pseudospectral methods for differential equations is presented. Properties of the classical orthogonal polynomials required in this context are reviewed. Differentiation matrices corresponding to Jacobi, Laguerre,and Hermite cases are constructed. A fairly detailed investigation is made for the Hermite spectral methods, which is applied to the Schrödinger eigenvalue equation with several potentials. A discussion of the numerical results and comparison with other methods are then ...
On the Krall-type polynomials on q-quadratic lattices
Alvarez-Nodarse, R.; Adiguzel, R. Sevinik (Elsevier BV, 2011-08-01)
In this paper, we study the Krall-type polynomials on non-uniform lattices. For these polynomials the second order linear difference equation, q-basic series representation and three-term recurrence relations are obtained. In particular, the q-Racah-Krall polynomials obtained via the addition of two mass points to the weight function of the non-standard q-Racah polynomials at the ends of the interval of orthogonality are considered in detail. Some important limit cases are also discussed. (C) 2011 Royal Net...
On the arithmetic of fibered surfaces
Kaba, Mustafa Devrim; Önsiper, Mustafa Hurşit; Department of Mathematics (2011)
In the first three chapters of this thesis we study two conjectures relating arithmetic with geometry, namely Tate and Lang’s conjectures, for a certain class of algebraic surfaces. The surfaces we are interested in are assumed to be defined over a number field, have irregularity two and admit a genus two fibration over an elliptic curve. In the final chapter of the thesis we prove the isomorphism of the Picard motives of an arbitrary variety and its Albanese variety.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
R. Sevindik-Adıgüzel, “On the q-analysis of q-hypergeometric difference equation,” Ph.D. - Doctoral Program, Middle East Technical University, 2010.