2012, Graduate studies in mathematics, ISBN 0821889869, Volume 142., x, 187

Book

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2018, Volume 466, Issue 1, pp. 1009 - 1042

In this paper we are interested in Euler-type sums with products of harmonic numbers, Stirling numbers and Bell numbers. We discuss the analytic...

Euler sums | Riemann zeta function | Multiple zeta (star) values | Stirling numbers | Harmonic numbers | Multiple harmonic (star) numbers | INTEGRALS | MATHEMATICS | MULTIPLE ZETA-VALUES | MATHEMATICS, APPLIED | SERIES

Euler sums | Riemann zeta function | Multiple zeta (star) values | Stirling numbers | Harmonic numbers | Multiple harmonic (star) numbers | INTEGRALS | MATHEMATICS | MULTIPLE ZETA-VALUES | MATHEMATICS, APPLIED | SERIES

Journal Article

2008, University lecture series, ISBN 9780821844113, Volume 41, viii, 167

Book

Mathematical and Computer Modelling, ISSN 0895-7177, 2011, Volume 54, Issue 9, pp. 2220 - 2234

Harmonic numbers and generalized harmonic numbers have been studied since the distant past and are involved in a wide range of diverse fields such as analysis...

Stirling numbers of the first kind | Generalized hypergeometric function [formula omitted] | Harmonic numbers | Polygamma functions | Generalized harmonic numbers | Riemann Zeta function | Psi function | Hurwitz Zeta function | Summation formulas for [formula omitted] | Riemann zeta function | Summation formulas for pfq | Generalized hypergeometric function pfq | Hurwitz zeta function | INFINITE SERIES | MATHEMATICS, APPLIED | IDENTITIES | HYPERGEOMETRIC-SERIES | GENERATING-FUNCTIONS | RIEMANN ZETA | Generalized hypergeometric function F-p(q) | SUMS | INTEGRALS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | ZETA-FUNCTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SERIES REPRESENTATIONS | Summation formulas for F-p(q) | Statistics | Analysis | Algorithms

Stirling numbers of the first kind | Generalized hypergeometric function [formula omitted] | Harmonic numbers | Polygamma functions | Generalized harmonic numbers | Riemann Zeta function | Psi function | Hurwitz Zeta function | Summation formulas for [formula omitted] | Riemann zeta function | Summation formulas for pfq | Generalized hypergeometric function pfq | Hurwitz zeta function | INFINITE SERIES | MATHEMATICS, APPLIED | IDENTITIES | HYPERGEOMETRIC-SERIES | GENERATING-FUNCTIONS | RIEMANN ZETA | Generalized hypergeometric function F-p(q) | SUMS | INTEGRALS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | ZETA-FUNCTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SERIES REPRESENTATIONS | Summation formulas for F-p(q) | Statistics | Analysis | Algorithms

Journal Article

Integral Transforms and Special Functions, ISSN 1065-2469, 07/2019, Volume 30, Issue 7, pp. 581 - 593

In this paper we will introduce a sequence of complex numbers that are called the Jacobi numbers. This sequence generalizes in a natural way several sequences...

33C45 | 11Y55 | 11B83 | generalized harmonic numbers | 11C20 | 11B65 | Catalan numbers | orthogonal Jacobi polynomial | Hankel determinant | MATHEMATICS | MATHEMATICS, APPLIED | COEFFICIENTS | ORTHOGONAL POLYNOMIALS | TRANSFORM | Complex numbers | Determinants | Polynomials

33C45 | 11Y55 | 11B83 | generalized harmonic numbers | 11C20 | 11B65 | Catalan numbers | orthogonal Jacobi polynomial | Hankel determinant | MATHEMATICS | MATHEMATICS, APPLIED | COEFFICIENTS | ORTHOGONAL POLYNOMIALS | TRANSFORM | Complex numbers | Determinants | Polynomials

Journal Article

Advanced Functional Materials, ISSN 1616-301X, 05/2017, Volume 27, Issue 19, pp. 1604468 - n/a

The quantum confinement in atomic scale and the presence of interlayer coupling in multilayer make the electronic and optical properties of 2D materials (2DMs)...

layer numbers | optical properties | thickness determination | international standardization | 2D materials | PHYSICS, CONDENSED MATTER | MONOLAYER MOS2 | PHYSICS, APPLIED | PHOTOLUMINESCENCE | INTERLAYER INTERACTIONS | MATERIALS SCIENCE, MULTIDISCIPLINARY | CHEMISTRY, PHYSICAL | NANOSCIENCE & NANOTECHNOLOGY | CHEMISTRY, MULTIDISCIPLINARY | TWISTED MULTILAYER GRAPHENE | TRANSITION-METAL DICHALCOGENIDES | 2ND-HARMONIC GENERATION | RESONANT RAMAN-SPECTROSCOPY | BLACK PHOSPHORUS | SHEAR MODES | VALLEY POLARIZATION | Raman spectroscopy | Optical properties | Quantum confinement | Second harmonic generation | Interlayers | Rayleigh scattering | Standardization | Photoluminescence | Optics | Flakes | Chemical vapor deposition | Substrates | Two dimensional materials

layer numbers | optical properties | thickness determination | international standardization | 2D materials | PHYSICS, CONDENSED MATTER | MONOLAYER MOS2 | PHYSICS, APPLIED | PHOTOLUMINESCENCE | INTERLAYER INTERACTIONS | MATERIALS SCIENCE, MULTIDISCIPLINARY | CHEMISTRY, PHYSICAL | NANOSCIENCE & NANOTECHNOLOGY | CHEMISTRY, MULTIDISCIPLINARY | TWISTED MULTILAYER GRAPHENE | TRANSITION-METAL DICHALCOGENIDES | 2ND-HARMONIC GENERATION | RESONANT RAMAN-SPECTROSCOPY | BLACK PHOSPHORUS | SHEAR MODES | VALLEY POLARIZATION | Raman spectroscopy | Optical properties | Quantum confinement | Second harmonic generation | Interlayers | Rayleigh scattering | Standardization | Photoluminescence | Optics | Flakes | Chemical vapor deposition | Substrates | Two dimensional materials

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 11/2019, Volume 15, Issue 10, pp. 2179 - 2200

In this paper, we prove three congruences involving Apéry-like numbers D n , S n and T n which have been conjectured by Sun. These numbers are defined by D n =...

POLYNOMIALS | MATHEMATICS | Apery-like numbers | Domb numbers | APERY | Harmonic numbers | PROOF | congruences | BERNOULLI | SUMS

POLYNOMIALS | MATHEMATICS | Apery-like numbers | Domb numbers | APERY | Harmonic numbers | PROOF | congruences | BERNOULLI | SUMS

Journal Article

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, ISSN 1015-8634, 05/2019, Volume 56, Issue 3, pp. 649 - 658

In this paper, we prove some congruences involving the generalized Catalan numbers and harmonic numbers modulo p(2), one of which is Sigma(p-1)(k=1)...

MATHEMATICS | harmonic numbers and binomial coefficients | congruences | IDENTITIES

MATHEMATICS | harmonic numbers and binomial coefficients | congruences | IDENTITIES

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2011, Volume 218, Issue 3, pp. 734 - 740

Harmonic numbers and generalized harmonic numbers have been studied since the distant past and involved in a wide range of diverse fields such as analysis of...

Stirling numbers of the first kind | Harmonic numbers | Summation formulas for pFq | Polygamma functions | Generalized harmonic numbers | Psi-function | Riemann Zeta function | Generalized hypergeometric function pFq | Hurwitz Zeta function | Summation formulas for | Generalized hypergeometric function | GAMMA | MATHEMATICS, APPLIED | IDENTITIES | HYPERGEOMETRIC-SERIES | GENERATING-FUNCTIONS | Generalized hypergeometric function F-p(q) | SUMS | INTEGRALS | Riemann Zeta function, Hurwitz Zeta function | ZETA-FUNCTION | SERIES REPRESENTATIONS | Summation formulas for F-p(q) | EULER | Statistics | Analysis | Algorithms | Hypergeometric functions | Harmonics | Mathematical analysis | Infinite series | Elementary particles | Mathematical models | Number theory

Stirling numbers of the first kind | Harmonic numbers | Summation formulas for pFq | Polygamma functions | Generalized harmonic numbers | Psi-function | Riemann Zeta function | Generalized hypergeometric function pFq | Hurwitz Zeta function | Summation formulas for | Generalized hypergeometric function | GAMMA | MATHEMATICS, APPLIED | IDENTITIES | HYPERGEOMETRIC-SERIES | GENERATING-FUNCTIONS | Generalized hypergeometric function F-p(q) | SUMS | INTEGRALS | Riemann Zeta function, Hurwitz Zeta function | ZETA-FUNCTION | SERIES REPRESENTATIONS | Summation formulas for F-p(q) | EULER | Statistics | Analysis | Algorithms | Hypergeometric functions | Harmonics | Mathematical analysis | Infinite series | Elementary particles | Mathematical models | Number theory

Journal Article

Turkish Journal of Mathematics, ISSN 1300-0098, 2019, Volume 43, Issue 1, pp. 340 - 354

It has been known that some numbers, including Bernoulli, Cauchy, and Euler numbers, have such corresponding numbers in terms of determinants of Hessenberg...

Determinants | Convolutions | Hyperharmonic numbers | Recurrence relations | Harmonic numbers | MATHEMATICS | recurrence relations | determinants | IDENTITIES | BERNOULLI | FORMULAS | hyperharmonic numbers | convolutions

Determinants | Convolutions | Hyperharmonic numbers | Recurrence relations | Harmonic numbers | MATHEMATICS | recurrence relations | determinants | IDENTITIES | BERNOULLI | FORMULAS | hyperharmonic numbers | convolutions

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2019, Volume 42, Issue 18, pp. 7030 - 7046

The aim of this paper is to introduce and investigate some of the primary generalizations and unifications of the Peters polynomials and numbers by means of...

Peters numbers and polynomials | Apostoly‐type numbers and polynomials | harmonic sums and numbers | Euler numbers and polynomials | generating function | Bernoulli numbers and polynomials | p‐adic integral | Stirling numbers | Cauchy numbers and polynomials | MATHEMATICS, APPLIED | p-adic integral | APOSTOL-TYPE NUMBERS | FAMILIES | CONSTRUCTION | Apostoly-type numbers and polynomials | Functions (mathematics) | Interpolation | Functional equations | Mathematical analysis | Integrals | Polynomials | Markov analysis | Identities | Combinatorial analysis | Sums

Peters numbers and polynomials | Apostoly‐type numbers and polynomials | harmonic sums and numbers | Euler numbers and polynomials | generating function | Bernoulli numbers and polynomials | p‐adic integral | Stirling numbers | Cauchy numbers and polynomials | MATHEMATICS, APPLIED | p-adic integral | APOSTOL-TYPE NUMBERS | FAMILIES | CONSTRUCTION | Apostoly-type numbers and polynomials | Functions (mathematics) | Interpolation | Functional equations | Mathematical analysis | Integrals | Polynomials | Markov analysis | Identities | Combinatorial analysis | Sums

Journal Article

Journal of Number Theory, ISSN 0022-314X, 07/2019, Volume 200, pp. 397 - 406

Let vn be the denominator of the n-th harmonic number Hn=1+2−1+⋯+n−1. In this paper, we prove the following unusual result: the set of positive integers n with...

Denominators | Alternating harmonic numbers | Harmonic numbers | Asymptotic density | MATHEMATICS

Denominators | Alternating harmonic numbers | Harmonic numbers | Asymptotic density | MATHEMATICS

Journal Article

Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 03/2019, Volume 23, pp. 187 - 193

Özet: Bu çalışmada$H_{z}^{(w)}=\frac{\left( z\right) _{w}}{z\Gamma\left( w\right) }\left( \Psi\left( z+w\right) -\Psi\left( w\right) \right)$where $\text{ \ \...

Digamma fonksiyonu | Hiperharmonik sayılar | Digamma function | Harmonik sayılar | Beta fonksiyonu | Harmonic numbers | Beta function | Gamma function | Gamma fonksiyonu | Hyperharmonic numbers

Digamma fonksiyonu | Hiperharmonik sayılar | Digamma function | Harmonik sayılar | Beta fonksiyonu | Harmonic numbers | Beta function | Gamma function | Gamma fonksiyonu | Hyperharmonic numbers

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 09/2019, Volume 269, pp. 77 - 85

Recently, by using methods of hypercomplex function theory, the authors have shown that a certain sequence S of rational numbers (Vietoris’ sequence) combines...

Hypercomplex Appell polynomials | Generating function | Recurrence relation | Vietoris’ number sequence | ORTHOGONAL APPELL SYSTEMS | POLYNOMIALS | MATHEMATICS, APPLIED | EXPONENTIALS | Vietoris' number sequence | Numbers | Sequences | Analytic functions | Mathematical analysis | Harmonic analysis | Fourier analysis | Polynomials

Hypercomplex Appell polynomials | Generating function | Recurrence relation | Vietoris’ number sequence | ORTHOGONAL APPELL SYSTEMS | POLYNOMIALS | MATHEMATICS, APPLIED | EXPONENTIALS | Vietoris' number sequence | Numbers | Sequences | Analytic functions | Mathematical analysis | Harmonic analysis | Fourier analysis | Polynomials

Journal Article

IEEE Transactions on Power Electronics, ISSN 0885-8993, 11/2004, Volume 19, Issue 6, pp. 1586 - 1593

Power quality problems associated with distributed power (DP) inverters, implemented in large numbers onto the same distribution network, are investigated....

Pulse width modulation inverters | Power measurement | Network topology | Photovoltaic cells | Power quality | Laboratories | photovoltaic (PV) | Power system harmonics | Harmonic analysis | Distributed power (DP) | Power harmonic filters | Power generation | Photovoltaic (PV) | distributed power (DP) | ENGINEERING, ELECTRICAL & ELECTRONIC | Electric inverters | Research | Management | Harmonics (Electric waves) | Electric power distribution | Solar cells | Harmonics | Networks | Penetration | Computer simulation | Electronics | Inverters | Topology

Pulse width modulation inverters | Power measurement | Network topology | Photovoltaic cells | Power quality | Laboratories | photovoltaic (PV) | Power system harmonics | Harmonic analysis | Distributed power (DP) | Power harmonic filters | Power generation | Photovoltaic (PV) | distributed power (DP) | ENGINEERING, ELECTRICAL & ELECTRONIC | Electric inverters | Research | Management | Harmonics (Electric waves) | Electric power distribution | Solar cells | Harmonics | Networks | Penetration | Computer simulation | Electronics | Inverters | Topology

Journal Article

Discrete Mathematics, ISSN 0012-365X, 10/2017, Volume 340, Issue 10, pp. 2388 - 2397

In this paper, we consider combinatorial numbers (Cm,k)m≥1,k≥0, mentioned as Catalan triangle numbers where Cm,k≔m−1k−m−1k−1. These numbers unify the entries...

Combinatorial identities | Catalan numbers | Catalan triangle | Binomial coefficients | MATHEMATICS | IDENTITIES | SUMMATION | HARMONIC NUMBERS

Combinatorial identities | Catalan numbers | Catalan triangle | Binomial coefficients | MATHEMATICS | IDENTITIES | SUMMATION | HARMONIC NUMBERS

Journal Article

Energy Conversion and Management, ISSN 0196-8904, 2009, Volume 50, Issue 11, pp. 2761 - 2767

In this paper, a new topology of cascaded multilevel inverter using a reduced number of switches, insulated gate driver circuits and voltage standing on...

Cascaded multilevel inverter | H-bridge | Sub-multilevel inverter | Full-bridge | Multilevel inverter | MECHANICS | HARMONIC ELIMINATION | THERMODYNAMICS | ENERGY & FUELS | Control systems | Analysis | Algorithms

Cascaded multilevel inverter | H-bridge | Sub-multilevel inverter | Full-bridge | Multilevel inverter | MECHANICS | HARMONIC ELIMINATION | THERMODYNAMICS | ENERGY & FUELS | Control systems | Analysis | Algorithms

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2011, Volume 218, Issue 3, pp. 991 - 995

In the paper, we collect some inequalities and establish a sharp double inequality for bounding the n-th harmonic number.

Harmonic number | Sharp bound | Psi function | Inequality | MATHEMATICS, APPLIED | INEQUALITIES | POLYGAMMA FUNCTIONS | PSI | MONOTONIC FUNCTIONS | Harmonics | Mathematical models | Computation | Inequalities | Mathematics - Classical Analysis and ODEs

Harmonic number | Sharp bound | Psi function | Inequality | MATHEMATICS, APPLIED | INEQUALITIES | POLYGAMMA FUNCTIONS | PSI | MONOTONIC FUNCTIONS | Harmonics | Mathematical models | Computation | Inequalities | Mathematics - Classical Analysis and ODEs

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 2/2018, Volume 154, Issue 1, pp. 147 - 186

We extend Wolstenholme’s theorem to hyperharmonic numbers. Then, we obtain infinitely many congruence classes for hyperharmonic numbers using combinatorial...

5A10 | primary 11B83 | congruence identity | Mathematics, general | 11B75 | Mathematics | hyperharmonic number | harmonic number | MATHEMATICS | SPECIAL VALUES | ZETA-FUNCTION

5A10 | primary 11B83 | congruence identity | Mathematics, general | 11B75 | Mathematics | hyperharmonic number | harmonic number | MATHEMATICS | SPECIAL VALUES | ZETA-FUNCTION

Journal Article