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Öğe A New Generalization of Pochhammer Symbol and Its Applications(Walter De Gruyter Gmbh, 2020) Şahin, Recep; Yağcı, OğuzIn this paper, we introduce a new generalization of the Pochhammer symbol by means of the generalization of extended gamma function (4). Using the generalization of Pochhammer symbol, we give a generalization of the extended hypergeometric functions one or several variables. Also, we obtain various integral representations, derivative formulas and certain properties of these functions.Öğe Degenerate Pochhammer symbol, degenerate Sumudu transform, and degenerate hypergeometric function with applications(Hacettepe Univ, Fac Sci, 2021) Yağcı, Oğuz; Şahin, RecepIn the paper, we first define a degenerate Pochhammer symbol by using the degenerate gamma function and investigate its properties. By using the degenerate Pochhammer symbol, we introduce and investigate a degenerate hypergeometric function. We also define a degenerate Sumudu transform and investigate its properties by using degenerate exponential function. Finally, we give certain the integral representations, derivative formulas, integral transforms, factional calculus applications, and generating functions of the degenerate hypergeometric function.Öğe H ?1,?2,?3 A Srivastava Hypergeometric Function(2018) Şahin, Recep; Yağcı, OğuzFormulas and identities involving many well known special functions (such as the Gamma and Betafunctions, Gauss hypergeometric function, and so on) play important roles in themselves and their diverseapplications. In this paper, we will add ?1, ?2, ?3 parameters to the HA Srivastava hypergeometric functionand we introduce new H?1,?2,?3A Srivastava’s triple ? -hypergeometric function. Then, we present someproperties of the H?1,?2,?3A Srivastava’s triple ? -hypergeometric function.Öğe Note on the Hurwitz-Lerch Zeta Function of Two Variables(MDPI, 2020) Choi, Junesang; Şahin, Recep; Yağcı, Oğuz; Kim, DojinA number of generalized Hurwitz-Lerch zeta functions have been presented and investigated. In this study, by choosing a known extended Hurwitz-Lerch zeta function of two variables, which has been very recently presented, in a systematic way, we propose to establish certain formulas and representations for this extended Hurwitz-Lerch zeta function such as integral representations, generating functions, derivative formulas and recurrence relations. We also point out that the results presented here can be reduced to yield corresponding results for several less generalized Hurwitz-Lerch zeta functions than the extended Hurwitz-Lerch zeta function considered here. For further investigation, among possibly various more generalized Hurwitz-Lerch zeta functions than the one considered here, two more generalized settings are provided.Öğe On the matrix versions of Appell hypergeometric functions(Natl Inquiry Services Centre Pty Ltd, 2014) Altın, Abdullah; Çekim, Bayram; Şahin, RecepThe main aim of this paper is on Appell hypergeometric matrix functions. Also, matrix differential equations and integral representation satisfied F-1 matrix function is derived.Öğe Parabolik operatörler için maksimum prensibi ve doyum problemi(Kırıkkale Üniversitesi, 2004) Şahin, Recep; Olgun, Y.AliÖZET PARABOLİK OPERATÖRLER İÇİN MAKSİMUM PRENSİBİ VE DOYUM PROBLEMİ ŞAHİN, Recep Kırıkkale Üniversitesi Fen Bilimleri Enstitüsü Matematik Anabilim Dalı, Yüksek Lisans Tezi Danışman : Yrd.Doç. Dr. Ali OLGUN Temmuz 2004, 97 Sayfa Bu tez dört bölümden oluşmaktadır. Birinci bölümde; yapılan çalışmalar ve tezin genel amacı hakkında bilgiler verilmiştir. İkinci bölümde; maksimum prensibi, başlangıç ve sınır değer problemleri açıklanmıştır. Üçüncü bölümde; parabolik tipten denklemler için maksimum prensibi, ısı denklemi için maksimum prensibi ve ısı denklemi için patlama ve doyum problemleri incelenmiştir. Dördüncü bölüm ise tartışma ve sonuç olarak ayrılmıştır. Anahtar Kelimeler: Maksimum ve minimum nokta, maksimum ve minimum değer, sınır değer problemi, parabolik operatör, ısı denklemi. Patlama ve doyum problemiÖğe Recursion Formulas for Srivastava Hypergeometric Functions(Walter De Gruyter Gmbh, 2015) Şahin, RecepRecently, Opps, Saad and Srivastava have given the recursion formulas of Appell's function F-2 by the contiguous relation of the Gauss hypergeometric series F-2(1). Then, Wang has presented various recursion formulas for F-1, F-2, F-3 and F-4 Appell's hypergeometric functions. The aim of this paper is to present various recursion formulas for Srivastava hypergeometric functions by the contiguous relations of hypergeometric series. (C) 2015 Mathematical Institute Slovak Academy of SciencesÖğe Solution of fractional kinetic equations involving generalized Hurwitz-Lerch Zeta function using Sumudu transform(Ankara Univ, Fac Sci, 2021) Yağcı, Oğuz; Şahin, RecepFractional kinetic equations (FKEs) comprising a large array of special functions have been extensively and successfully applied in specification and solving many significant problems of astrophysics and physics. In this present work, our aim is to demonstrate solutions of (FKEs) of the generalized Hurwitz-Lerch Zeta function by applying the Sumudu transform. In addition to these, solutions of (FKEs) in special conditions of generalised Hurwitz-Lerch Zeta function have been derived.Öğe Some $k$-Horn hypergeometric functions and their properties(2023) Çatak, Caner; Şahin, Recep; Olgun, Ali; Yağcı, OğuzIn the theory of special functions, the $k$-Pochhammer symbol is a generalization of the Pochhammer symbol. With the help of the $k$-Pochhammer symbol, we introduce and study a new generalization of the $k$-Horn hypergeometric functions such as, ${G}_{1}^{k}$, ${G}_{2}^{k}$ and ${G}_{3}^{k}$. Furthermore, several investigations have been carried out for some important recursion formulae for several one variable and two variables $k$-hypergeometric functions. In the light of these studies, we introduce some important recursion formulae for several newly generalized $k$-Horn hypergeometric functions. Finally, we present several relations between some $k$-Horn hypergeometric functions ${G}_{1}^{k}$, ${G}_{2}^{k}$ and ${G}_{3}^{k}$, and $k$-Gauss hypergeometric functions $_{2}{F}_{1}^{k}$.
