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Title: | On q-Analogue and (p,q)–Analogue of Gamma and Beta Functions |
Authors: | Mahmudov, Nazım Al-Khateeb, Areen Saber Eastern Mediterranean University, Faculty of Arts and Sciences, Department of Mathematics |
Keywords: | Mathematics Department q-Gamma Function, q-Beta Function, (p,q)-Gamma Function, (p,q)-Beta Function |
Issue Date: | Jan-2017 |
Publisher: | Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ) |
Citation: | Al-Khateeb, Areen Saber. (2017). On q-Analogue and (p,q)–Analogue of Gamma and Beta Functions. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus. |
Abstract: | ABSTRACT: In this study we discuss the integral representation of the q-analogue of two special functions, q-GF (gamma function) and q-BF (beta function). This discussion gives a very attractive q-constant.Also, we get the proof of the famous Jacobi triple product which contains the identity of Jacobi .After that we obtain a new proof for Ramanujan’s equation. Furthermore, we introduce a new generalization of gamma function and beta function that are: the (p,q) - GF and the (p,q) - BF. Finally, we obtain an equivalent definitions for (p,q) - analogue for GF and BF.
Keywords: q-Gamma Function, q-Beta Function, (p,q)-Gamma Function, (p,q)-Beta Function. ÖZ: Bu çalışmada, iki özel fonksiyon, q-gama fonksiyonu ve q-beta fonksiyonunun integral formu tartışılmaktadır. Ayrıca, (p, q) -gamma fonksiyonun ve (p, q) - beta fonksiyonun yeni bir gama fonksiyonu ve beta fonksiyonu genellemesi elde edilmiştir. Son olarak, gama ve beta fonksiyonları için (p, q) - analog için eşdeğer tanımlar verilmiştir.
Anahtar kelimeler: q- gama fonksiyonu, q-beta fonksiyonunun, (p, q) -gamma fonksiyonun, (p, q) -beta fonksiyonun. |
Description: | Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2017. Supervisor: Prof. Dr. Nazım Mahmudov. |
URI: | http://hdl.handle.net/11129/4781 |
Appears in Collections: | Theses (Master's and Ph.D) – Mathematics
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