Yazar "Küçükoğlu, İrem" için listeleme
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Analysis of higher-order peters-type combinatorial numbers and polynomials by their generating functions and p-adic integration
Küçükoğlu, İrem (American Institute of Physics Inc., 2020)The aim of this paper is to analyze higher-order Peters-type combinatorial numbers and polynomials by means of their generating functions and p-adic integration. By using generating functions we first obtain a combinatorial ... -
An approach to negative hypergeometric distribution by generating function for special numbers and polynomials
Küçükoğlu, İrem; Şimşek, Burçin; Şimşek, Yılmaz (2019)The aim of this paper is to not only provide a definition of a new family of special numbers and polynomials of higher-order with their generating functions, but also to investigate their fundamental properties in the ... -
Computation of k-ary Lyndon words using generating functions and their differential equations
Küçükoğlu, İrem; Şimşek, Yılmaz (Univ Nis, Fac Sci Math, 2018)By using generating functions technique, we investigate some properties of the k-ary Lyndon words. We give an explicit formula for the generating functions including not only combinatorial sums, but also hypergeometric ... -
Derivative formulas related to unification of generating functions for sheffer type sequences
Küçükoğlu, İrem (Amer Inst Physics, 2019)The main aim of this paper is to present partial derivative formulas for an unification, which was introduced by the author in "Unification of the generating functions for Sheffer type sequences and their applications, ... -
Generating functions for new families of combinatorial numbers and polynomials: Approach to poisson-charlier polynomials and probability distribution function
Küçükoğlu, İrem; Şimşek, Burçin; Şimşek, Yılmaz (Mdpi, 2019)The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and differential equations, we not only ... -
Identities and derivative formulas for the combinatorial and apostol-euler type numbers by their generating functions
Küçükoğlu, İrem; Şimşek, Yılmaz (Univ Nis, Fac Sci Math, 2018)The first aim of this paper is to give identities and relations for a new family of the combinatorial numbers and the Apostol-Euler type numbers of the second kind, the Stirling numbers, the Apostol-Bernoulli type numbers, ... -
Identities for dirichlet and lambert-type series arising from the numbers of a certain special word
Küçükoğlu, İrem; Şimşek, Yılmaz (Univ Belgrade, Fac Electrical Engineering, 2019)The goal of this paper is to give several new Dirichlet-type series associated with the Riemann zeta function, the polylogarithm function, and also the numbers of necklaces and Lyndon words. By applying Dirichlet convolution ... -
Matrix representations for a certain class of combinatorial numbers associated with bernstein basis functions and cyclic derangements and their probabilistic and asymptotic
Küçükoğlu, İrem; Şimşek, Yılmaz (2021)In this paper, we mainly concerned with an alternate form of the generating functions for a certain class of combinatorial numbers and polynomials. We give matrix representations for these numbers and polynomials with their ... -
Multidimensional Bernstein polynomials and Bezier curves: Analysis of machine learning algorithm for facial expression recognition based on curvature
Küçükoğlu, İrem; Şimşek, Buket; Şimşek, Yilmaz (Elsevier Science Inc, 2019)In this paper, by using partial derivative formulas of generating functions for the multidimensional unification of the Bernstein basis functions and their functional equations, we derive derivative formulas and identities ... -
New classes of Catalan-type numbers and polynomials with their applications related to p-adic integrals and computational algorithms
Küçükoğlu, İrem; Şimşek, Burçin; Şimşek, Yılmaz (Scientific Technical Research Council Turkey-Tubitak, 2020)The aim of this paper is to construct generating functions for new classes of Catalan-type numbers and polynomials. Using these functions and their functional equations, we give various new identities and relations involving ... -
Numerical evaluation of special power series including the numbers of Lyndon words: an approach to interpolation functions for apostol-type numbers and polynomials
Küçükoğlu, İrem; Şimşek, Yılmaz (Kent State University, 2018)Because the Lyndon words and their numbers have practical applications in many different disciplines such as mathematics, probability, statistics, computer programming, algorithms, etc., it is known that not only mathematicians ... -
On a family of special numbers and polynomials associated with apostol-type numbers and poynomials and combinatorial numbers
Küçükoğlu, İrem; Şimşek, Yılmaz (Univ Belgrade, Fac Electrical Engineering, 2019)In this article, we examine a family of some special numbers and polynomials not only with their generating functions, but also with computation algorithms for these numbers and polynomials. By using these algorithms, we ... -
Remarks on recurrence formulas for the Apostol-type numbers and polynomials
Küçükoğlu, İrem; Şimşek, Yılmaz (Jangjeon Mathematical Society, 2018)In this paper, by differentiating the generating functions for one of the family of the Apostol-type numbers and polynomials with respect to their parameters, we present some partial differential equations including these ... -
Some new identities and formulas for higher-order combinatorial-type numbers and polynomials
Küçükoğlu, İrem (Univ Nis, Fac Sci Math, 2020)The main purpose of this paper is to provide various identities and formulas for higher-order combinatorial-type numbers and polynomials with the help of generating functions and their both functional equations and derivative ...
