dc.contributor.advisor |
Mahmudov, Nazim I. |
|
dc.contributor.author |
Keleshteri, Marzieh Eini |
|
dc.date.accessioned |
2019-04-25T12:47:44Z |
|
dc.date.available |
2019-04-25T12:47:44Z |
|
dc.date.issued |
2015-07 |
|
dc.date.submitted |
2015 |
|
dc.identifier.citation |
Keleshteri, Marzieh Eini (2015). A Comprehensive Study on the Class of q-Appell Polynomials . Thesis (Ph.D.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus. |
en_US |
dc.identifier.uri |
http://hdl.handle.net/11129/4041 |
|
dc.description |
Doctor of Philosophy in Mathematics. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr. Nazim Mahmudov. |
en_US |
dc.description.abstract |
This thesis is aimed to study the q-analogue of the class of so called Appell polynomials
from different aspects and using various algebraic as well as analytic approaches. To
achieve this aim, not only many new results are found based on a proposed general
generating function for all members belonging to the aforementioned family of polynomials,
but also various relations between famous members of this family are derived. 2D q-Appell
polynomials as the q-Appell polynomials in two variables can be considered as another new
achievement of this thesis. In addition to the definition of the class of q-Appell polynomials
by means of their generating function, a determinantal representation, for the first time, is
proposed for indicating different members of the class of q-Appell polynomials. Moreover,
it is shown that how easy some results can be proved by using the new proposed linear
algebraic indication and applying basic properties of determinant. In the sequel, this family
of q-polynomials are studied also from q-umbral point of view and many interesting results
are found based on this algebraic approach.
Keywords: q-Appell, q-Calculus, Determinatal, q-Umbral, q-Polynomilas, q-Apostol, q-
Bernoulli, q-Euler, q-Genocchi, q-Hermite. |
en_US |
dc.description.abstract |
Öz:Bu tez farklı açılardan ve çeşitli cebirsel yanı sıra analitik yaklaşımlar kullanarak q-Appell
polinomların sınıfının incelenmesini amaçlanmaktadır. Bu amaca ulaşmak için, yukarıda
belirtilen q-Appell polinomlar ailesine ait tüm üyeler üyeleri arasında çeşitli ilişkiler elde
edilmektedir. İki değişkenli q-Appell polinomları olarak 2D q-Appell polinomları bu tezin
yeni bir başarı olarak kabul edilebilir. Ayrıca, bazı sonuçlar yeni önerilen lineer cebirsel
gösterge kullanılarak ve determinantın temel özelliklerini uygulanarak ispat edilebilir.
Ayrıca, bu tezde q-polinomların birçok ilginç özellikleri q-umbral açısından da
incelenmiştir.
Anahtar Kelimeler: q-Appell, q-Matematik, q-Umbral, q-Polynomlar, q-Apostol, q-
Bernoulli, q-Euler, q-Genocchi, q-Hermite. |
en_US |
dc.language.iso |
eng |
en_US |
dc.publisher |
Eastern Mediterranean University EMU |
en_US |
dc.rights |
info:eu-repo/semantics/openAccess |
en_US |
dc.subject |
Mathematics |
en_US |
dc.subject |
q-Appell |
en_US |
dc.subject |
q-Umbral |
en_US |
dc.subject |
q-Polynomilas |
en_US |
dc.subject |
q-Apostol |
en_US |
dc.subject |
q-Bernoulli |
en_US |
dc.subject |
q-Euler |
en_US |
dc.subject |
q-Genocchi |
en_US |
dc.subject |
q-Hiteerm |
en_US |
dc.subject |
Determinatal |
en_US |
dc.subject |
q-Calculus |
en_US |
dc.title |
A Comprehensive Study on the Class of q-Appell Polynomials |
en_US |
dc.type |
doctoralThesis |
en_US |
dc.contributor.department |
Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics |
en_US |