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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.
Giuseppe Dattoli +3 more
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Summation Formulas Involving Binomial Coefficients, Harmonic Numbers, and Generalized Harmonic Numbers [PDF]
Abstract and Applied Analysis, 2014 A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of ...
Junesang Choi
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Harmonic numbers, harmonic series and zeta function [PDF]
Moroccan Journal of Pure and Applied Analysis, 2018 This paper reviews, from different points of view, results on Bernoulli numbers and polynomials, the distribution of prime numbers in connexion with the Riemann hypothesis. We give an account on the theorem of G. Robin, as formulated by J. Lagarias.
Sebbar Ahmed
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On the denominators of harmonic numbers. IV [PDF]
Comptes Rendus. Mathématique, 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 $1, 2, \dots , n$.
Wu, Bing-Ling, Yan, Xiao-Hui
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On Harmonic Complex Balancing Numbers
Mathematics, 2022 In the present work, we define harmonic complex balancing numbers by considering well-known balancing numbers and inspiring harmonic numbers. Mainly, we investigate some of their basic characteristic properties such as the Binet formula and Cassini ...
Fatih Yılmaz +2 more
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Lerch-harmonic numbers related to Lerch transcendent
Mathematical and Computer Modelling of Dynamical Systems, 2023 Harmonic numbers and generalized harmonic numbers have been studied in connection with combinatorial problems, many expressions involving special functions in analytic number theory and analysis of algorithms.
Taekyun Kim +3 more
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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
Hagis, Peter jun., Lord, Graham
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One Type of Symmetric Matrix with Harmonic Pell Entries, Its Inversion, Permanents and Some Norms
Mathematics, 2021 The Pell numbers, named after the English diplomat and mathematician John Pell, are studied by many authors. At this work, by inspiring the definition harmonic numbers, we define harmonic Pell numbers.
Seda Yamaç Akbiyik +2 more
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Polynomials related to harmonic numbers and evaluation of harmonic number series II [PDF]
Applicable Analysis and Discrete Mathematics, 2011 In this paper we focus on r-geometric polynomials, r-exponential polynomials and their harmonic versions. It is shown that harmonic versions of these polynomials and their generalizations are useful to obtain closed forms of some series related to harmonic numbers. 2000 Mathematics Subject Classification. 11B73, 11B75, 11B83.
Dil, Ayhan, Kurt, Veli
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Proceedings - Mathematical Sciences, 2021 The harmonic sums \(\sum_{r=k+1}^n \frac{1}{r}\) are not integers for any \(k \geq 1\). One way of proving this uses the Bertrand postulate that there is always a prime strictly between \(k\) and \(2k\) if \(k \geq 2\). The paper under review considers the more general analogous sums \(h_K(n) := \sum_{r=1}^n \frac{a_r}{r}\) where \(a_r\) is the number ...
Çağatay Altuntaş, Haydar Göral
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