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Title: | Classical Orthogonal Polynomials and Differential Operators |
Authors: | Oğurlu, Sonuç Zorlu Onbaşı, İlkay Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics |
Keywords: | Mathematics Orthogonal polynomials-Mathematics-Calculus Classical orthogonal polynomials hypergeometric function second order differential equation Rodrigues formula |
Issue Date: | Jan-2017 |
Publisher: | Eastern Mediterranean University EMU - Doğu Akdeniz Üniversitesi (DAÜ) |
Citation: | Onbaşı, İlkay. (2017). Classical Orthogonal Polynomials and Differential Operators. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus. |
Abstract: | In this thesis we introduce the concept of classical orthogonal polynomials which are Hermite, Laguerre and Jacobi polynomials. We first provide the necessary overview on special functions. Then we give several properties of orthogonal polynomials in Chapter 2. In Chapter 3, we start to classical orthogonal polynomials firstly we obtain the orthogonality relation, Rodrigues formulas and we give the norm of the classical orthogonal polynomials. Finally we divide the examples of classical orthogonal polynomials into three chapters and for each of them we give the weight function, interval of the orthogonality, second order differential equation, hypergeometric representation. Keywords: classical orthogonal polynomials, hypergeometric function, second order differential equation, Rodrigues formula. ÖZ:
Bu tezde klasik ortogonal polinomlar olan Hermite, Laguerre ve Jacobi polinomları tanımlanmıştır. İlk olarak özel fonksiyonlar hakkında ön bilgi verilmiştir. İkinci bölümde ortogonal polinomların bazı özellikleri çalışılmıştır. Üçüncü bölümde klasik ortogonal polinomlar tanımlanmış ve ilk olarak ortogonallik ilişkisi, Rodrigues formülü verilmiş ve klasik ortogonal polinomlar için norm hesabı yapılmıştır. Son olarak klasik ortogonal polinom örnekleri 3 bölüme ayrılmış ve herbiri için ağırlık fonksiyonları, ortogonallik aralığı, ikinci dereceden diferansiyel denklemi ve hipergeometrik gösterimi verilmiştir.
Anahtar Kelimeler: Klasik ortogonal polinomlar, hipergeometrik fonksiyon, ikinci dereceden diferansiyel denklem, Rodrigues formülü. |
Description: | Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2017. Supervisor: Prof. Dr. Sonuç Zorlu Oğurlu. |
URI: | http://hdl.handle.net/11129/4344 |
Appears in Collections: | Theses (Master's and Ph.D) – Mathematics
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