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Öğe A note on Shively’s Pseudo-Laguerre Polynomials(Murat TOSUN, 2019) Özmen, NejlaIn this research, we esteblish some properties for the Shively’s Pseudo-Laguerre polynomials. We derive various families of multilinear and multilateral generating functions for a family of Shively’s Pseudo-Laguerre polynomials.Öğe BILATERAL AND BILINEAR GENERATING FUNCTIONS FOR THE MODIFIED GENERALIZED SYLVESTER POLYNOMIALS(Univ Nis, 2018) Özmen, NejlaThe present study deals with some new properties for the modified generalized Sylvester polynomials. The results obtained here include various families of multilinear and multilateral generating functions, miscellaneous properties and also some special cases for these polynomials. In addition, we derive a theorem giving certain families of bilateral generating functions for the modified generalized Sylvester polynomials and the generalized Lauricella functions. Finally, we get several interesting results of this theorem.Öğe AN EXTENSION OF A CLASS OF GENERATING FUNCTIONS FOR THE CESARO POLYNOMIALS OF THREE VARIABLES(Editura Bibliotheca-Bibliotheca Publ House, 2018) Özmen, Nejla; Duman, Esra ErkuşThe present study deals with some new properties for the Cesaro polynomials of three variables. The results obtained here include various families of multilinear and multilateral generating functions and their miscellaneous properties. We also derive an application giving certain families of bilateral generating functions for the Cesaro polynomials and the generalized Lauricella functions. At the end, we discuss some special cases for this theorem.Öğe Gegenbauer Polinomları İçin Bilineer ve Bilateral Doğurucu Fonksiyonlar(2018) Özmen, NejlaBu çalışma Gegenbauer (veya ultraküresel) polinomları için bilineer ve bilateral doğurucu fonksiyonlarla ilgilidir. Gegenbauer polinomları için bazı özel durumları, çeşitli özelliklerini, multilinear ve multilateral doğurucu fonksiyonları elde edilmiştir.Öğe Generalized Gould-Hopper Polynomials(Mehmet Zeki SARIKAYA, 2021) Özmen, Nejla; Topaloğlu, MustafaIn this paper, we derive generating functions for the generalized Gould-Hopper polynomials in terms of the generalized Lauricella function by using series rearrangement techniques. Further, we derive the summation formulae for that polynomials by using different analytical means on its generating function or by using certain operational techniques. Also, generating functions and summation formulae for the polynomials related to generalized Gould-Hopper polynomials are obtained as applications of main results. In addition, we derive a theorem giving certain families of bilateral generating functions for the generalized Gould-Hopper polynomials. The results obtained here include various families of bilinear and bilateral generating functions, miscellaneous properties and also some special cases for these polynomials.Öğe Generalized Sylvester Polynomials of in Several Variables(Prairie View A & M Univ, Dept Mathematics, 2018) Özmen, Nejla; Soytürk, ŞuleThis study deals with some new properties for the Generalized Sylvester polynomials in several variables. Some properties of these polynomials were given. We also derive an application giving certain families of bilateral generating functions for the Generalized Sylvester polynomials in several variables. At the end, we discuss some special cases.Öğe Miscellaneous Properties of Generalized Fubini Polynomials(Emrah Evren KARA, 2023) Ağca, Muhammet; Özmen, NejlaThis article attempts to present the generalized Fubini polynomials $F_{n}(x,y,z,q)$. The results obtained here include various families of multilinear and multilateral generating functions, various properties, as well as some special cases for these generalized Fubini polynomials $F_{n}(x,y,z,q)$. Finally, we get several interesting results of this generalized Fubini polynomials and obtain an integral representation.Öğe New Generating Function Relations for the q-Generalized Cesaro Polynomials(Hindawi Ltd, 2019) Özmen, NejlaThe main purpose of this paper is to examine a basic (or q-) analogue of the generalized Cesaro polynomials described here. We derive a bilateral q-generating function involving basic analogue of Fox's H-function and q-generalized Cesaro polynomials.Öğe On Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers(2021) Özmen, Nejla; Soykan, YükselIn this paper, we present Binet's formulas, generating functions, and the summation formulas for generalized Hexanacci numbers, and as special cases, we investigate Hexanacci and Hexanacci-Lucas numbers with their properties. Also, we define Gaussian generalized Hexanacci numbers and as special cases, we investigate Gaussian Hexanacci and Gaussian Hexanacci-Lucas numbers with their properties. Moreover, we give some identities for these numbers. Furthermore, we present matrix formulations of generalized Hexanacci numbers and Gaussian generalized Hexanacci numbers.Öğe On Generalized Sister Celine's Polynomials(Murat TOSUN, 2019) Özmen, NejlaIn this research, we establish some properties for the generalized Sister Celine's polynomials. We derive various families of multilinear and multilateral generating functions for a family of generalized Sister Celine's polynomials.Öğe On the Generalized Sylvester Polynomials(Springer International Publishing, 2019) Özmen, Nejla; Duman, Esra ErkuşIn this study, we give some new properties for the generalized Sylvester polynomials. The results obtained here include various families of multilinear and multilateral generating functions and miscellaneous properties. In addition, we derive a theorem giving certain families of bilateral generating functions for the generalized Sylvester polynomials and the Lauricella functions. Finally, we get several results of this theorem. © Springer Nature Switzerland AG 2019.Öğe ON THE GOTTLIEB POLYNOMIALS IN SEVERAL VARIABLES(Univ Nis, 2019) Duman, Esra Erkuş; Özmen, NejlaIn this study, we give some new properties of the Gottlieb polynomials in several variables. The results obtained here include various families of multilinear and multilateral generating functions, integral representation and recurrence relations for these polynomials. In addition, we derive a theorem giving certain families of bilateral generating functions for the multivariable Gottlieb polynomials and the generalized Lauricella functions. Finally, we get several results of this theorem.Öğe On The Konhauser Biorthogonal Polynomials(Matematikçiler Derneği, 2017) Özmen, Nejla; Cin, YahyaIn this study, we give new properties of the Konhauser biorthogonal polynomials $Y_{n}^{\alpha }(x;k)$. Various families of multilinear, multilateral generating functions, some special cases and several recurrence relations for these polynomials are obtained.Öğe On The Mittag-Leffler Polynomials and Deformed Mittag-Leffler Polynomials(Mehmet Zeki SARIKAYA, 2019) Özmen, Nejla; Yılmaz, NihalThe present study deals with some new properties for the Mittag-Leffler polynomials and the deformed Mittag-Leffler polynomials. The results obtained here include various families of multilinear and multilateral generating functions, miscellaneous properties and also some special cases for these polynomials.Öğe Some families of generating functions for the generalized cesàro polynomials(Eudoxus Press, LLC, 2018) Özmen, Nejla; Duman, Esra ErkuşThe present study deals with some new properties for the generalized Cesàro polynomials. The results obtained here include various families of multilinear and multilateral generating functions, miscellaneous properties and also some special cases for these polynomials. In addition, we derive a theorem giving certain families of bilateral generating functions for the generalized Cesàro polynomials and the generalized Lauricella functions. Finally, we get several interesting results of this theorem. © 2018 by Eudoxus Press, LLC. All rights reserved.Öğe Some Generating Functions for a Class of Hypergeometric Polynomials(Gazi Univ, 2018) Özmen, Nejla; Duman, Esra ErkuşThis article concerned with some new features for hypergeometric polynomials S-k((alpha, beta)) (x). The results obtained here contain the various families of multilinear and multilateral generating functions, various features and some exceptions for these polynomials. We will also give a theorem to families giving certain bilateral generating functions for hypergeometric polynomials S-k((alpha, beta)) (x) and generalized Lauricella functions. Finally, we get a few interesting results for this Hypergeometric given theorem.Öğe Some New Generating Functions for the Modified Laguerre Polynomials(Global Science Press, 2019) Özmen, NejlaIn this paper, we obtain some new results on bilateral generating functions of the modified Laguerre polynomials. We also get generating function relations between the modified Laguerre polynomials and the generalized Lauricella functions. Some special cases and important applications are also discussed.Öğe Some new properties of generalized bessel polynomials(Polish Academy of Sciences, Institute of Mathematics, 2019) Özmen, NejlaWe obtain some new properties of generalized Bessel polynomials. We mainly investigate bilinear and bilateral generating function relations for these polynomials. We also derive a result giving certain families of bilateral generating functions for generalized Bessel polynomials and generalized Lauricella functions. We also discuss some special cases. © Instytut Matematyczny PAN, 2019.Öğe Some new properties of the Meixner polynomials(2017) Özmen, NejlaThe present study deals with some new properties for the Meixner polynomials. In this manuscript weobtain a number of families of bilinear and bilateral generating functions, general properties and also somespecial cases for these polynomials. In addition, we derive a theorem giving certain families of bilateralgenerating functions for the generalized Lauricella functions and the Meixner polynomials. Finally, we getseveral interesting results of this theorem.Öğe Some new properties of the Meixner polynomials(Sakarya University, 2017) Özmen, NejlaThe present study deals with some new properties for the Meixner polynomials. In this manuscript we obtain a number of families of bilineer and bilateral generating functions, general properties and also some special cases for these polynomials. In addition, we derive a theorem giving certain families of bilateral generating functions for the generalized Lauricella functions and the Meixner polynomials. Finally, we get several interesting results of this theorem.
