Results 181 to 190 of about 120,275 (213)
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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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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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On the matrices with harmonic numbers
2010In 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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On the Ramanujan Harmonic Number Expansion
Results in Mathematics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Harmonic Numbers of Any Order and the Wolstenholme’s-Type Relations for Harmonic Numbers
2016The 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 +5 more
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Extremal values on the harmonic number of trees
International Journal of Computer Mathematics, 2014Let 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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Inequalities for the harmonic numbers
Mathematische Zeitschrift, 2009Let \(H_n:=1+\frac 12+\dots+\frac 1n,n\geq 1\), be the harmonic numbers. The author proves the following. For all integers \(n\geq 2\), it holds that \[ \alpha\frac{\log(\log n +\gamma)}{n^2}\leq H_n^{\frac 1n}-H_{n+1}^{\frac{1}{n+1}}
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Evolving an Harmonic Number Generator with ReNCoDe
2013Evolutionary Algorithms (EA) are loosely inspired in the ideas of natural selection and genetics. Over the years some researchers have advocated the need of incorporating more ideas from biology into EAs, in particular with respect to the individuals’ representation and the mapping from the genotype to the phenotype.
Rui L. Lopes, Ernesto Costa
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Milliwatt terahertz harmonic generation from topological insulator metamaterials
Light: Science and Applications, 2022+2 more
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Review of AI applications in harmonic analysis in power systems
Renewable and Sustainable Energy Reviews, 2022Ahmadreza Eslami +2 more
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