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Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 10/2019, Volume 13, Issue 2, pp. 478 - 494
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... 
MATHEMATICS | Apostol-type numbers and polynomials | MATHEMATICS, APPLIED | Generating functions | Combinatorial numbers | BERNOULLI | Stirling numbers | EULER | Computation algorithm
Journal Article
Filomat, ISSN 0354-5180, 1/2016, Volume 30, Issue 4, pp. 985 - 992
In [3], Simsek unified generating function of the Bernstein basis functions. In this paper, by using knot sequence, we rewrite generating functions for the... 
Generating function | Mathematical functions | Hermite numbers | Binomial coefficients | Gamma and Beta functions | Bernstein type polynomials | Laplace transform | Knot sequence | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | Binomial coefficients, Gamma and Beta functions | BERNOULLI
Journal Article
Filomat, ISSN 0354-5180, 2018, Volume 32, Issue 10, pp. 3455 - 3463
By using generating functions technique, we investigate some properties of the k-ary Lyndon words. We give an explicit formula for the generating functions... 
Apostol-Bernoulli numbers and polynomials | Lyndon words | Ordinary differential equations | Stirling numbers | Algorithm | Generating functions | MATHEMATICS, APPLIED | NECKLACES | Q-EXTENSIONS | BERNOULLI | BEADS | MATHEMATICS | EULER POLYNOMIALS
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 07/2019, Volume 2116, Issue 1
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... 
Mathematical analysis | Polynomials
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 03/2019, Volume 344-345, pp. 150 - 162
In this paper, by using partial derivative formulas of generating functions for the multidimensional unification of the Bernstein basis functions and their... 
Statistical evaluations | Facial expression recognition | Bezier curve | Generating function | Bernstein basis function | Machine learning | MATHEMATICS, APPLIED | GENERATING-FUNCTIONS | Algorithms | Data mining | Analysis | Differential equations
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 07/2018, Volume 1978, Issue 1
The aim of this paper is to give some combinatorial sums, identities and relations related to a family of combinatorial numbers and the Bernstein type basis... 
functional equations | binomial coefficients | special numbers | gamma function | beta function | Bernstein basis functions | generating functions | combinatorial sum | combinatorial identity | special functions | Numbers | Basis functions | Functional equations | Mathematical analysis | Combinatorial analysis | Sums
Journal Article
Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 1/2019, Volume 13, Issue 3, pp. 787 - 804
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... 
Lyndon words | MATHEMATICS, APPLIED | Dirichlet convolution | Generating function | Lambert series | Necklace polynomial | BERNOULLI | Apostol-Bernoulli numbers | MATHEMATICS | Polylogarithm | Number-theoretic function | Dirichlet series | EULER
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 07/2017, Volume 1863, Issue 1
The main aim of this paper is to construct ordinary generating functions for the numbers of k-ary Lyndon words of length prime. We give combinatorial aspect of... 
Combinatorial analysis | Markov analysis
Journal Article
Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 2019, Volume 13, Issue 2, pp. 478 - 494
Journal Article
ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, ISSN 1068-9613, 2018, Volume 50, pp. 98 - 108
Because the Lyndon words and their numbers have practical applications in many different disciplines such as mathematics, probability, statistics, computer... 
Lyndon words | Apostol-type numbers and polynomials | arithmetical function | ZETA | MATHEMATICS, APPLIED | FAMILIES | special numbers and polynomials | interpolation function | BERNOULLI | zeta type function | EULER NUMBERS
Journal Article
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, ISSN 0304-9914, 01/2019, Volume 56, Issue 1, pp. 265 - 284
The main purpose of this paper is to investigate the q-Apostol type Frobenius-Euler numbers and polynomials. By using generating functions for these numbers... 
Q-ANALOG | MATHEMATICS, APPLIED | Frobenius-Euler numbers | Euler numbers | l(q)-series | TWISTED L-FUNCTIONS | generating functions | BERNOULLI | Apostol-Bernoulli numbers | Apostol-Euler numbers | MATHEMATICS | multiplication formula | ZETA | special numbers and polynomials | q-Apostol type Frobenius-Euler numbers and polynomials
Journal Article
06/2018
The aim of this paper is to define some new number-theoretic functions including necklaces polynomials and the numbers of special words such as Lyndon words.... 
Mathematics - Number Theory
Journal Article
10/2017
Recently, the numbers $Y_{n}(\lambda )$ and the polynomials $Y_{n}(x,\lambda)$ have been introduced by the second author [22]. The purpose of this paper is to... 
Mathematics - Number Theory
Journal Article
Annals of Telecommunications, ISSN 0003-4347, 4/2017, Volume 72, Issue 3, pp. 209 - 219
Journal Article
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