Yazar "Şimşek, Yılmaz" için listeleme
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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 ... -
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 ... -
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 ...
