Results 291 to 300 of about 11,335,757 (341)

A binomial sum of harmonic numbers

Discrete Mathematics, 2023
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Harmonic-number summation identities, symmetric functions, and multiple zeta values

The Ramanujan journal, 2016
We show how infinite series of a certain type involving generalized harmonic numbers can be computed using a knowledge of symmetric functions and multiple zeta values.
Michael E. Hoffman
semanticscholar   +1 more source

Summation of Harmonic Numbers

1989
The problem of finding closed forms for a summation involving harmonic numbers is considered. Solutions for ∑ i n =1P(i)H i (k) , where p(i) is a polynomial, and ∑ i n =1 Hi/(i+m), where m is an integer, are given. A method to automate these results is presented.
Dominic Y. Savio, Edmund A. Lamagna, Shing-Min Liu   +2 more
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On the denominators of harmonic numbers, II

Journal of Number Theory, 2019
The \textit{harmonic number} \(H_n\) is defined as \(\sum_{i=1}^n \frac{1}{i}\) and the \textit{alternating harmonic number} \(A_n\) is defined as \(\sum_{i=1}^n (-1)^{i+1}\frac{1}{i}\). Write \(H_n=\frac{u_n}{v_n}\) with \(\gcd(u_n,v_n)=1\), \(v_n>0\); and \(A_n=\frac{a_n}{b_n}\) with \(\gcd(a_n,b_n)=1\), \(b_n>0\).
Bing-Ling Wu, Yong-Gao Chen
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Certain summation formulas involving harmonic numbers and generalized harmonic numbers

Applied Mathematics and Computation, 2011
New identities about certain finite or infinite series involving harmonic numbers and generalized harmonic numbers are established.
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On Generalized Harmonic Numbers

2021
For three positive integers a, b and n, let \(H_{a,b}(n)\) be the sum of the reciprocals of the first n terms of arithmetic progression \(\{ ak+b : k=0,1, \ldots \} \) and let \(v_{a,b} (n)\) be the denominator of \(H_{a,b}(n).\) In this paper, we prove that for two coprime positive integers a and b, (i) if p is a prime with \(p\not \mid a\), then the ...
Yong-Gao Chen, Bing-Ling Wu
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On the matrices with harmonic numbers

2010
In this study, firstly we define nxn matrices P and Q associated with harmonic numbers such that and Q where k Hk is denote kth harmonic number. After we study the spectral norms, Euclidean norms and determinants of these matrices.
BAHSİ, Mustafa, SOLAK, Süleyman
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Research on Characteristic Airgap Harmonics of a Double-Rotor Flux-Modulated PM Motor Based on Harmonic Dimensionality Reduction

IEEE Transactions on Transportation Electrification
In this article, a method of dimension reduction analysis of airgap harmonics is proposed and investigated for a double-rotor flux-modulated permanent magnet (DR-FMPM) motor. By analyzing the relationships among the torque, core loss, and power factor of
Zixuan Xiang, Yuting Zhou, Xiaoyong Zhu, L. Quan, Deyang Fan, Qian Liu   +5 more
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Harmonic Numbers of Any Order and the Wolstenholme’s-Type Relations for Harmonic Numbers

2016
The concept of harmonic numbers has appeared permanently in the mathematical science since the very early days of differential and integral calculus. Firsts significant identities concerning the harmonic numbers have been developed by Euler (see Basu, Ramanujan J, 16:7–24, 2008, [1], Borwein and Bradley, Int J Number Theory, 2:65–103, 2006, [2], Sofo ...
Edyta Hetmaniok, Piotr Lorenc, Mariusz Pleszczyński, Michał Różański, Marcin Szweda, Roman Wituła   +5 more
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Extremal values on the harmonic number of trees

International Journal of Computer Mathematics, 2014
Let G=VG, EG be a simple connected graph. The harmonic number of G, denoted by HG, is defined as the sum of the weights 2/du+dv of all edges uv of G, where du denotes the degree of a vertex u in G. In this paper, some extremal problems on the harmonic number of trees are studied.
Qiong Fan, Shuchao Li, Qin Zhao
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