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On the denominators of harmonic numbers, II
Journal of Number Theory, 2019The \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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On generalized harmonic number sums
Applied Mathematics and Computation, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mark W. Coffey, Nicholas Lubbers
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Identities on harmonic and q-harmonic number sums
Afrika Matematika, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Ramanujan’s formula for the harmonic number
Applied Mathematics and Computation, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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 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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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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