Results 21 to 30 of about 95 (80)

Hyperharmonic Numbers Can Rarely Be Integers

Integers, 2018
See the abstract in the attached pdf.
Emre Alkan, Haydar Göral, Doga Can Sertbas   +2 more
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Identities involving harmonic and hyperharmonic numbers [PDF]

Advances in Difference Equations, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kim, Dae San, Kim, Taekyun
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On shifted Mascheroni series and hyperharmonic numbers

Journal of Number Theory, 2016
In this article, we study the nature of the forward shifted series σ r = n>r |bn| n−r where r is a positive integer and b n are Bernoulli numbers of the second kind, expressing them in terms of the derivatives ζ (−k) of zeta at the negative integers and Euler's constant γ.
Coppo, Marc-Antoine, Young, Paul Thomas
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A Combinatorial Approach to Hyperharmonic numbers

, 2003
Hyperharmonic numbers arise by taking repeated partial sums of harmonic numbers. These numbers can be expressed in terms of r-Stirling numbers, leading to combinatorial interpretations of many interesting identities.
Benjamin, Arthur T., Gaebler, David, Gaebler, Robert   +2 more
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Sums of powers of integers and hyperharmonic numbers [PDF]

Notes on Number Theory and Discrete Mathematics, 2021
In this paper, we obtain a new formula for the sums of k-th powers of the first n positive integers, Sk(n), that involves the hyperharmonic numbers and the Stirling numbers of the second kind. Then, using an explicit representation for the hyperharmonic numbers, we generalize this formula to the sums of powers of an arbitrary arithmetic progression ...
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Euler sums of generalized alternating hyperharmonic numbers II

The Ramanujan Journal, 2021
33 ...
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Some Identities of Harmonic and Hyperharmonic Fibonacci Numbers

Gazi University Journal of Science, 2021
This paper is concerned with the combinatorial identities of the harmonic and the hyperharmonic Fibonacci numbers. By using the symmetric algorithm, we get some identities which improve the usual results and generalize known equations. Moreover, with the help of concept of Riordan array, we obtain the generating functions for these numbers and a ...
Miraç ÇETİN, Can KIZILATEŞ, Fatma YEŞİL BARAN, Naim TUGLU   +3 more
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Evaluation of cauchy polynomials via degenerate r-Stirling numbers

Mathematical and Computer Modelling of Dynamical Systems
In this paper, within the framework of unsigned degenerate [Formula: see text]-Stirling numbers, we establish connections among Cauchy polynomials, degenerate Bernoulli polynomials, and degenerate hyperharmonic numbers.
Zhuoyu Chen, Yuankui Ma, Taekyun Kim, Dae San Kim, Yanan Hei   +4 more
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Series involving degenerate harmonic numbers and degenerate Stirling numbers

Applied Mathematics in Science and Engineering
Recently, degenerate harmonic numbers and degenerate hyperharmonic numbers are introduced by Kim-Kim. In this paper, we study the series involving the degenerate harmonic numbers and degenerate Stirling numbers and investigate those properties.
Lingling Luo, Yuankui Ma, Taekyun Kim, Rongrong Xu   +3 more
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On the norms of circulant and r-circulant matrices with the hyperharmonic Fibonacci numbers [PDF]

Journal of Inequalities and Applications, 2015
In this paper, we study norms of circulant and $r-$circulant matrices involving harmonic Fibonacci and hyperharmonic Fibonacci numbers. We obtain inequalities by using matrix norms.
KIZILATEŞ, CAN, TUĞLU, NAİM
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