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