Results 11 to 20 of about 640,777 (319)
Series of Convergence Rate −1/4 Containing Harmonic Numbers
Axioms, 2023 Two general transformations for hypergeometric series are examined by means of the coefficient extraction method. Several interesting closed formulae are shown for infinite series containing harmonic numbers and binomial/multinomial coefficients.
Chunli Li, Wenchang Chu
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Unitary Harmonic Numbers [PDF]
Proceedings of the American Mathematical Society, 1975 If d ∗ ( n ) {d^ \ast }(n) and σ ∗ ( n ) {\sigma ^ \ast }(n) denote the number and sum, respectively, of the unitary divisors of the natural number n n
Graham Lord, Peter Hagis
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On the denominators of harmonic numbers, III [PDF]
Periodica Mathematica Hungarica, 2022 Let $\mathcal{L}$ be the set of all positive integers $n$ such that the denominator of $1+1/2+\cdots +1/n$ is less than the least common multiple of $1, 2, \dots , n$. In this paper, under a certain assumption on linear independence, we prove that the set $\mathcal{L}$ has the upper asymptotic density $1$.
Wu, Bing-Ling, Yan, Xiao-Hui
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Infinite series about harmonic numbers inspired by Ramanujan–like formulae
Electronic Research Archive, 2023 By employing the coefficient extraction method from hypergeometric series, we shall establish numerous closed form evaluations for infinite series containing central binomial coefficients and harmonic numbers, including several conjectured ones made by Z.
Chunli Li, Wenchang Chu
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On the harmonic and hyperharmonic Fibonacci numbers [PDF]
Advances in Difference Equations, 2015 In this paper, we study the theory of the harmonic and the hyperharmonic Fibonacci numbers. Also, we get some combinatoric identities like as harmonic and hyperharmonic numbers and we obtain some useful formulas for $\mathbb{F}_{n}$, which is finite sums of reciprocals of Fibonacci numbers.
KESİM, SEYHUN +2 more
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The sum of the telescoping series formed by reciprocals of the cubic polynomials with three different negative integer roots [PDF]
Mathematics in Education, Research and Applications, 2020 This paper deals with the sum of a special telescoping series and is a free follow-up to author’s preceding paper. The terms of this series are reciprocals of the cubic polynomial with three different negative integer roots.
Radovan Potůček
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Infinitary harmonic numbers [PDF]
Bulletin of the Australian Mathematical Society, 1990 The infinitary divisors of a natural number n are the products of its divisors of the , where py is an exact prime-power divisor of n and (where yα = 0 or 1) is the binary representation of y. Infinitary harmonic numbers are those for which the infinitary divisors have integer harmonic mean.
Peter Hagis, Graeme L. Cohen
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On the denominators of harmonic numbers
Comptes Rendus. Mathématique, 2018 6 ...
Bing-Ling Wu, Yong-Gao Chen
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Umbral Methods and Harmonic Numbers
Axioms, 2018 The theory of harmonic-based functions is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.
Dattoli G. +3 more
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