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

MATHEMATICS | Apostol-type numbers and polynomials | MATHEMATICS, APPLIED | Generating functions | Combinatorial numbers | BERNOULLI | Stirling numbers | EULER | Computation algorithm

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 1/2019, Volume 113, Issue 1, pp. 281 - 297

The aim of this paper is to construct interpolation functions for the numbers of the k-ary Lyndon words which count n digit primitive necklace class...

Lyndon words | 03D40 | Arithmetical functions | Special polynomials | Frobenius–Euler numbers and polynomials | 11S40 | Theoretical, Mathematical and Computational Physics | 11M35 | Generating functions | 68R15 | Mathematics | Algorithm | 11A25 | 11B68 | Stirling numbers of the first kind | 47E05 | 11B83 | Mathematics, general | Apostol–Euler numbers and polynomials | Differential operator | Applications of Mathematics | Special numbers | 05A05 | 05A15 | MATHEMATICS | Apostol-Euler numbers and polynomials | BERNOULLI | Frobenius-Euler numbers and polynomials | Operators (mathematics) | Interpolation | Algorithms | Infinite series | Combinatorial analysis | Sums

Lyndon words | 03D40 | Arithmetical functions | Special polynomials | Frobenius–Euler numbers and polynomials | 11S40 | Theoretical, Mathematical and Computational Physics | 11M35 | Generating functions | 68R15 | Mathematics | Algorithm | 11A25 | 11B68 | Stirling numbers of the first kind | 47E05 | 11B83 | Mathematics, general | Apostol–Euler numbers and polynomials | Differential operator | Applications of Mathematics | Special numbers | 05A05 | 05A15 | MATHEMATICS | Apostol-Euler numbers and polynomials | BERNOULLI | Frobenius-Euler numbers and polynomials | Operators (mathematics) | Interpolation | Algorithms | Infinite series | Combinatorial analysis | Sums

Journal Article

3.
Full Text
A Note on Generating Functions for the Unification of the Bernstein Type Basis Functions

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

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

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

Filomat, ISSN 0354-5180, 2018, Volume 32, Issue 20, pp. 6879 - 6891

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...

Arithmetical functions | Combinatorial sums | Bell numbers | Binomial coefficients | Functional equations | Partial differential equations | λ-Bernoulli numbers | Euler numbers of the second kind | Generating functions | Apostol-Euler type polynomials of the second kind | Stirling numbers of the second kind | lambda-Bernoulli numbers | MATHEMATICS, APPLIED | SUMS | MATHEMATICS

Arithmetical functions | Combinatorial sums | Bell numbers | Binomial coefficients | Functional equations | Partial differential equations | λ-Bernoulli numbers | Euler numbers of the second kind | Generating functions | Apostol-Euler type polynomials of the second kind | Stirling numbers of the second kind | lambda-Bernoulli numbers | MATHEMATICS, APPLIED | SUMS | MATHEMATICS

Journal Article

Axioms, ISSN 2075-1680, 10/2019, Volume 8, Issue 4, p. 112

The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with...

cauchy numbers | binomial coefficients | bernstein basis functions | bernoulli numbers | daehee numbers and polynomials | generating functions | euler numbers | stirling numbers | poisson-charlier polynomials | bell polynomials | functional equations | p-adic integral | special numbers and polynomials | probability distribution | partial differential equations | combinatorial sums

cauchy numbers | binomial coefficients | bernstein basis functions | bernoulli numbers | daehee numbers and polynomials | generating functions | euler numbers | stirling numbers | poisson-charlier polynomials | bell polynomials | functional equations | p-adic integral | special numbers and polynomials | probability distribution | partial differential equations | combinatorial sums

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

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

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

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

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

Combinatorial analysis | Markov analysis

Journal Article

Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 2019, Volume 13, Issue 2, pp. 478 - 494

Journal Article

Advanced Studies in Contemporary Mathematics (Kyungshang), ISSN 1229-3067, 2018, Volume 28, Issue 1, pp. 41 - 56

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

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

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

Journal of Number Theory, ISSN 0022-314X, 12/2017, Volume 181, pp. 117 - 146

The main motivation of this paper is to investigate some derivative properties of the generating functions for the numbers Yn(λ) and the polynomials Yn(x;λ),...

Hypergeometric functions | Apostol–Bernoulli numbers and Apostol–Bernoulli polynomials | Humbert polynomials | Partial differential equations | Binomial coefficients | Generating functions | Apostol–Euler numbers and Apostol–Bernoulli polynomials | Daehee and Changhee numbers | Hurwitz–Lerch zeta functions | Cauchy numbers | Stirling numbers of the first kind | Functional equations | Lucas numbers | Hurwitz Lerch zeta functions | BERNOULLI NUMBERS | UNIFIED PRESENTATION | Apostol-Bernoulli polynomials | MATHEMATICS | Apostol-Euler numbers and | EULER POLYNOMIALS | Apostol-Bernoulli numbers and | 2ND KIND | FORMULAS | Medicine, Experimental | Medical research | Medical colleges | Statistics | Differential equations

Hypergeometric functions | Apostol–Bernoulli numbers and Apostol–Bernoulli polynomials | Humbert polynomials | Partial differential equations | Binomial coefficients | Generating functions | Apostol–Euler numbers and Apostol–Bernoulli polynomials | Daehee and Changhee numbers | Hurwitz–Lerch zeta functions | Cauchy numbers | Stirling numbers of the first kind | Functional equations | Lucas numbers | Hurwitz Lerch zeta functions | BERNOULLI NUMBERS | UNIFIED PRESENTATION | Apostol-Bernoulli polynomials | MATHEMATICS | Apostol-Euler numbers and | EULER POLYNOMIALS | Apostol-Bernoulli numbers and | 2ND KIND | FORMULAS | Medicine, Experimental | Medical research | Medical colleges | Statistics | Differential equations

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 12/2017, Volume 14, Issue 6, pp. 1 - 16

The main motivation of this paper was to give finite and infinite generating functions for the numbers of the k-ary Lyndon words and necklaces. In order to...

Lyndon words | Apostol–Bernoulli numbers and polynomials | Arithmetical function | 03D40 | Generating function | 11M35 | 68R15 | Mathematics | Special numbers and polynomials | 11A25 | 11B68 | Hurwitz–Lerch zeta function | Necklaces | 11B83 | Mathematics, general | Bernoulli numbers and polynomials | 05A15 | Stirling numbers of the second kind | MATHEMATICS, APPLIED | Hurwitz-Lerch zeta function | UNIFIED PRESENTATION | FORMULA | Apostol-Bernoulli numbers and polynomials | MATHEMATICS | EULER | Jewelry

Lyndon words | Apostol–Bernoulli numbers and polynomials | Arithmetical function | 03D40 | Generating function | 11M35 | 68R15 | Mathematics | Special numbers and polynomials | 11A25 | 11B68 | Hurwitz–Lerch zeta function | Necklaces | 11B83 | Mathematics, general | Bernoulli numbers and polynomials | 05A15 | Stirling numbers of the second kind | MATHEMATICS, APPLIED | Hurwitz-Lerch zeta function | UNIFIED PRESENTATION | FORMULA | Apostol-Bernoulli numbers and polynomials | MATHEMATICS | EULER | Jewelry

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

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

Mathematics - Number Theory

Journal Article

Annals of Telecommunications, ISSN 0003-4347, 4/2017, Volume 72, Issue 3, pp. 209 - 219

The Internet evolved from a network with a few terminals to an intractable network of millions of nodes. Recent interest in information-centric networks (ICNs)...

Engineering | Information and Communication, Circuits | Signal,Image and Speech Processing | Elliptical model | Communications Engineering, Networks | Virtual Data Repeater | Information Systems and Communication Service | R & D/Technology Policy | Future Internet | Computer Communication Networks | Information-centric networks | Traffic characterization | NETWORKS | TELECOMMUNICATIONS | Case studies | Models | Internet | Analysis

Engineering | Information and Communication, Circuits | Signal,Image and Speech Processing | Elliptical model | Communications Engineering, Networks | Virtual Data Repeater | Information Systems and Communication Service | R & D/Technology Policy | Future Internet | Computer Communication Networks | Information-centric networks | Traffic characterization | NETWORKS | TELECOMMUNICATIONS | Case studies | Models | Internet | Analysis

Journal Article

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.