17 citations · 59 across the 17 of their papers we have counts for
18 papers
Partial Deranged Bell Numbers and Their Combinatorial Properties
Yahia Djemmada, Levent Kargın, Mümün Can
We introduce a novel generalization of deranged Bell numbers by defining the partial deranged Bell numbers , which count the number of set partitions of …
On certain harmonic zeta functions
Mümün Can, Levent Kargın, Mehmet Cenkci +1
This study deals with certain harmonic zeta functions, one of them occurs in the study of the multiplication property of the harmonic Hurwitz zeta function. The values at the negat…
On the Stieltjes constants with respect to harmonic zeta functions
Levent Kargın, Ayhan Dil, Mehmet Cenkci +1
The aim of this paper is to investigate harmonic Stieltjes constants occurring in the Laurent expansions of the function \[ ζ_{H}\left( s,a\right) =\sum_{n=0}^{\infty}\frac{1}{\lef…
Stieltjes constants appearing in the Laurent expansion of the hyperharmonic zeta function
Mümün Can, Ayhan Dil, Levent Kargın
In this paper, we consider meromorphic extension of the function \[ ζ_{h^{\left( r\right) }}\left( s\right) =\sum_{k=1}^{\infty} \frac{h_{k}^{\left( r\right) }}{k^{s}},\text{ }\ope…
Generalizations of the Euler-Mascheroni constant associated with the hyperharmonic numbers
Mümün Can, Ayhan Dil, Levent Kargın +2
In this paper, we present two new generalizations of the Euler-Mascheroni constant arising from the Dirichlet series associated to the hyperharmonic numbers. We also give some ineq…
On Evaluations of Euler-type Sums of Hyperharmonic Numbers
Levent Kargın, Mümün Can, Ayhan Dil +1
We give explicit evaluations of the linear and non-linear Euler sums of hyperharmonic numbers with reciprocal binomial coefficients. These evaluations en…
New series with Cauchy and Stirling numbers, Part 2
Khristo N. Boyadzhiev, Levent Kargın
We evaluate in closed form several series involving products of Cauchy numbers with other special numbers (harmonic, skew-harmonic, hyperharmonic, and central binomial). Similar re…
Generalized harmonic numbers via poly-Bernoulli polynomials
Levent Kargın, Mehmet Cenkci, Ayhan Dil +1
We present a relationship between the generalized hyperharmonic numbers and the poly-Bernoulli polynomials, motivated from the connections between harmonic and Bernoulli numbers. T…
Euler sums of generalized harmonic numbers and connected extensions
Mümün Can, Levent Kargın, Ayhan Dil +1
This paper presents the evaluation of the Euler sums of generalized hyperharmonic numbers \[ ζ_{H^{\left( p,q\right) }}\left( r\right) =\sum\limits_{n=…
Formulas for sums of powers of integers and their reciprocals
Levent Kargın, Ayhan Dil, Mümün Can
This paper gives new explicit formulas for sums of powers of integers and their reciprocals.
Polynomials with r-Lah coefficient and hyperharmonic numbers
Levent Kargın, Mümün Can
In this paper, we take advantage of the Mellin type derivative to produce some new families of polynomials whose coefficients involve r-Lah numbers. One of these polynomials leads…
Recurrences and Congruences for Higher order Geometric Polynomials and Related Numbers
Levent Kargın, Mehmet Cenkci
We obtain new recurrence relations, an explicit formula, and convolution identities for higher order geometric polynomials. These relations generalize known results for geometric p…
On the generating function of p-Bernoulli numbers: an alternative approach
Levent Kargın, Mourad Rahmani
In this note, we give an alternative proof of the generating function of -Bernoulli numbers. Our argument is based on the Euler's integral representation.
New results on p-Bernoulli numbers
Levent Kargın
We realize that geometric polynomials and p-Bernoulli polynomials and numbers are closely related with an integral representation. Therefore, using geometric polynomials, we extend…
A closed formula for the generating function of p-Bernoulli numbers
Levent Kargın, Mourad Rahmani
In this paper, using geometric polynomials, we obtain a generating function of p-Bernoulli numbers. As a consequences this generating function, we derive closed formulas for the fi…
Higher order generalized geometric polynomials
Levent Kargin, Bayram Çekim
According to generalized Mellin derivative (Kargin), we introduce a new family of polynomials called higher order generalized geometric polynomials. We obtain some properties of th…
Some formulae for products of Fubini polynomials with applications
Levent Kargın
In this paper we evaluate sums and integrals of products of Fubini polynomials and have new explicit formulas for Fubini polynomials and numbers. As a consequence of these results…
A new Generating Function of Exponential Polynomials and its Applications to the Related Polynomials and Numbers
Levent Kargın
In this paper we use computational method based on operational point of view to prove a new generating function of exponential polynomials. We give its applications involving geome…