Zobrazeno 1 - 10
of 70
pro vyhledávání: '"Dil, Ayhan"'
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 negative even integers are found and Laurent expansions at poles are descri
Externí odkaz:
http://arxiv.org/abs/2403.07123
The aim of this paper is to investigate harmonic Stieltjes constants occurring in the Laurent expansions of the function \[ \zeta_{H}\left( s,a\right) =\sum_{n=0}^{\infty}\frac{1}{\left( n+a\right) ^{s}}\sum_{k=0}^{n}\frac{1}{k+a},\text{ }\operatorna
Externí odkaz:
http://arxiv.org/abs/2304.03517
Publikováno v:
Applicable Analysis and Discrete Mathematics, 2023 Oct 01. 17(2), 401-417.
Externí odkaz:
https://www.jstor.org/stable/27281418
In this paper, we consider meromorphic extension of the function \[ \zeta_{h^{\left( r\right) }}\left( s\right) =\sum_{k=1}^{\infty} \frac{h_{k}^{\left( r\right) }}{k^{s}},\text{ }\operatorname{Re}\left( s\right) >r, \] (which we call \textit{hyperha
Externí odkaz:
http://arxiv.org/abs/2112.14047
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 inequalities related to upper and lower estimates, and evaluation formulas
Externí odkaz:
http://arxiv.org/abs/2109.01515
We give explicit evaluations of the linear and non-linear Euler sums of hyperharmonic numbers $h_{n}^{\left( r\right) }$ with reciprocal binomial coefficients. These evaluations enable us to extend closed form formula of Euler sums of hyperharmonic n
Externí odkaz:
http://arxiv.org/abs/2103.11876
Autor:
Aliev, Ilham A., Dil, Ayhan
Explicit evaluations of the Tornheim-like double series in the form \[ \sum_{n,m=1}^\infty \frac{H_{n+m+s}}{nm\left( n+m+s \right)},\ s\in \mathbb{N\cup } \left\{ 0 \right\} \] and their extensions are given. Furthermore, series of the type \[ \sum_{
Externí odkaz:
http://arxiv.org/abs/2008.02488
We present a relationship between the generalized hyperharmonic numbers and the poly-Bernoulli polynomials, motivated from the connections between harmonic and Bernoulli numbers. This relationship yields numerous identities for the hyper-sums and sev
Externí odkaz:
http://arxiv.org/abs/2008.00284
This paper gives new explicit formulas for sums of powers of integers and their reciprocals.
Externí odkaz:
http://arxiv.org/abs/2006.01132
This paper presents the evaluation of the Euler sums of generalized hyperharmonic numbers $H_{n}^{\left( p,q\right) }$ \[ \zeta_{H^{\left( p,q\right) }}\left( r\right) =\sum\limits_{n=1}^{\infty }\dfrac{H_{n}^{\left( p,q\right) }}{n^{r}}% \] in terms
Externí odkaz:
http://arxiv.org/abs/2006.00620