Results 1 to 10 of about 98,048 (175)
AppliedMathBased on a recent representation of the psi function due to Guillera and Sondow and independently Boyadzhiev, new closed forms for various series involving harmonic numbers and inverse factorials are derived.
Kunle Adegoke, Robert Frontczak
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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
Hagis, Peter jun., Lord, Graham
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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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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.
Hagis, Peter jun., Cohen, Graeme L.
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Harmonic numbers and finite groups [PDF]
Rendiconti del Seminario Matematico della Università di Padova, 2014 Given a finite group G , let {\tau} (G) be the number of normal subgroups of G ...
Baishya, Sekhar Jyoti, Das, Ashish Kumar
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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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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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