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Gauss's theorem and harmonic number summation formulae with certain mathematical constants
Journal of difference equations and applications (Print), 2019By computing the higher-order derivative of the famous Gauss hypergeometric summation theorem, we derive many harmonic number summation formulae with certain mathematical constants such as π, the Euler-Mascheroni constant γ, the Catalan constant G and ...
Hongmei Liu, Weiping Wang
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On Generalized Harmonic Numbers
2021For 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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Harmonic-number summation identities, symmetric functions, and multiple zeta values
, 2016We 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
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Certain summation formulas involving harmonic numbers and generalized harmonic numbers
Applied Mathematics and Computation, 2011New identities about certain finite or infinite series involving harmonic numbers and generalized harmonic numbers are established.
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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 +2 more
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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 +2 more
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Some Results for Generalized Harmonic Numbers
Integers, 2009AbstractIn this paper, we discuss the properties of a class of generalized harmonic ...
Feng, Congjiao, Zhao, Fengzhen
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Infinite Series Containing Generalized Harmonic Numbers
Results in Mathematics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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 +5 more
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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 +5 more
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Infinite Series involving skew harmonic numbers
Bulletin of the Belgian Mathematical Society - Simon StevinThere exist many infinite series identities involving harmonic \( H_{n}=\sum_{k=1}^{n}\frac{1}{k}\) and skew-harmonic numbers \( O_{n}=\sum_{k=1}^{n}\frac{1}{2k-1}\) in the literature. In the study [\textit{X. Wang} and \textit{W. Chu}, Rocky Mt. J. Math. 52, No.
Li, Chunli, Chu, Wenchang
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Infinite Series Identities on Harmonic Numbers
Results in Mathematics, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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