Zobrazeno 1 - 10
of 17
pro vyhledávání: '"Ayhan Dil"'
Publikováno v:
The Ramanujan Journal.
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a71cf02245055834aeb79f8c5209f354
https://doi.org/10.1007/s11139-022-00676-z
https://doi.org/10.1007/s11139-022-00676-z
Publikováno v:
Bulletin of the Malaysian Mathematical Sciences Society. 45:113-131
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6e0d69ff6682043f3c45846b0488a298
https://doi.org/10.1007/s40840-021-01179-8
https://doi.org/10.1007/s40840-021-01179-8
Publikováno v:
Lithuanian Mathematical Journal. 60:9-24
We give new proofs of some known results on the values of the Riemann zeta function at positive integers and obtain some new theorems related to these values. Considering even zeta values as ζ(2n) = ηnπ2n, we obtain the generating functions of the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::616733e17f2ae1dfc019a6d934aa5181
https://doi.org/10.1007/s10986-019-09456-7
https://doi.org/10.1007/s10986-019-09456-7
Autor:
Ayhan Dil
Publikováno v:
Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi
In this paper we investigate some properties of Hyperharmonic function defined$H_{z}^{(w)}=\frac{\left( z\right) _{w}}{z\Gamma\left( w\right) }\left(\Psi\left( z+w\right) -\Psi\left( w\right) \right)$where $\text{ \ \ }w\text{, }z+w\in\mathbb{C}\back
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::987af0a801b7293af8391233fbbfbf04
https://doi.org/10.19113/sdufenbed.453758
https://doi.org/10.19113/sdufenbed.453758
Autor:
Ayhan DİL
Publikováno v:
Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Vol 23, Pp 187-193 (2019)
Özet: Bu çalışmada$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{ \ \ }w\text{, }z+w\in\mathbb{C}\backslash\left( \mathbb{Z}^{-}\cup\left\{ 0\right\} \right)
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doajarticles::ac8e24c112554209d3df3e4aa8d8b69c
http://dergipark.org.tr/sdufenbed/issue/43548/453758?publisher=sdu-1
http://dergipark.org.tr/sdufenbed/issue/43548/453758?publisher=sdu-1
Autor:
Khristo N. Boyadzhiev, Ayhan Dil
Publikováno v:
Analysis Mathematica. 42:203-224
We provide several properties of the geometric polynomials discussed in earlier works of the authors. Further, the geometric polynomials are used to obtain a closed form evaluation of certain series involving Riemann's zeta function.
Comment: 18
Comment: 18
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::63385e717c5a6797ce944ee20d6ff489
https://doi.org/10.1007/s10476-016-0302-y
https://doi.org/10.1007/s10476-016-0302-y
Autor:
Erkan Muniroğlu, Ayhan Dil
In this study, depending on the upper and the lower indices of the hyperharmonic number $h_{n}^{(r)}$, nonlinear recurrence relations are obtained. It is shown that generalized harmonic number and hyperharmonic number can be obtained from derivatives
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::83a96deacb8009bf51f4ffb832f56ae1
Publikováno v:
Volume: 41, Issue: 6 1640-1655
Turkish Journal of Mathematics
Turkish Journal of Mathematics
In this paper we collect two generalizations of harmonic numbers (namelygeneralized harmonic numbers and hyperharmonic numbers) under one roof.Recursion relations, closed-form evaluations, and generating functions of thisunified extension are obtaine
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5ec2af644254ec49204f3e5c4b204bee
https://dergipark.org.tr/tr/pub/tbtkmath/issue/35842/401787
https://dergipark.org.tr/tr/pub/tbtkmath/issue/35842/401787
Autor:
Khristo N. Boyadzhiev, Ayhan Dil
We obtain a series transformation formula involving the classical Hermite polynomials. We then provide a number of applications using appropriate binomial transformations. Several of the new series involve Hermite polynomials and harmonic numbers, Lu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::81c150b42af80b9d167d92641a0c0c15
http://arxiv.org/abs/1710.00687
http://arxiv.org/abs/1710.00687
Autor:
István Mező, Ayhan Dil
Publikováno v:
Open Mathematics, Vol 7, Iss 2, Pp 310-321 (2009)
In this paper we use the Euler-Seidel method for deriving new identities for hyperharmonic and r-Stirling numbers. The exponential generating function is determined for hyperharmonic numbers, which result is a generalization of Gosper’s identity. A
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bdfc3a1431eccc2ade8dbe58e06f122d
https://doaj.org/article/4c522ed2f6ab4ec9b920e51883cd448e
https://doaj.org/article/4c522ed2f6ab4ec9b920e51883cd448e