Results 21 to 30 of about 351,945 (274)
Some Identities with Special Numbers
Cumhuriyet Science Journal, 2022 In this paper, we derive new identities which are related to some special numbers and generalized harmonic numbers H_n (α) by using the argument of the generating function given in [3] and comparing the coefficients of the generating functions.
Sibel Koparal +2 more
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Odd harmonic numbers exceed 10²⁴ [PDF]
Mathematics of Computation, 2010 A numbern>1n>1is harmonic ifσ(n)∣nτ(n)\sigma (n)\mid n\tau (n), whereτ(n)\tau (n)andσ(n)\sigma (n)are the number of positive divisors ofnnand their sum, respectively. It is known that there are no odd harmonic numbers up to101510^{15}. We show here that, for any odd numbern>106n>10^6,τ(n)≤n1/3\tau (n)\le n^{1/3}.
Cohen, Graeme L., Sorli, Ronald M.
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Sums involving the binomial coefficients, Bernoulli numbers of the second kind and harmonic numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 We offer a number of various finite and infinite sum identities involving the binomial coefficients, Bernoulli numbers of the second kind and harmonic numbers. For example, among many others, we prove Σⁿₖ₌ₒ((-1)ᵏhₖ/4ᵏ)$binom{2k}{k}$Gₙ₋ₖ = ((-1)ⁿ⁻¹/2^²ⁿ⁻¹)
Necdet Batır, Anthony Sofo
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Some sharp inequalities involving Seiffert and other means and their concise proofs [PDF]
, 2012 In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide concise proofs of some known inequalities and find some new sharp inequalities involving the Seiffert, contra-harmonic ...
Jiang, Wei-Dong, Qi, Feng
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Harmonic Manifolds and Tubes [PDF]
, 2017 The authors showed in a preceding paper that in a connected locally harmonic manifold, the volume of a tube of small radius about a regularly parameterized simple arc depends only on the length of the arc and the radius.
Csikós, Balázs, Horváth, Márton
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Some identities involving harmonic numbers [PDF]
Mathematics of Computation, 1990 Let H n {H_n} denote the nth harmonic number. Explicit formulas for sums of the form ∑ a k H k \sum {a_k}{H_k} or ∑ a
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Some results on q-harmonic number sums
Advances in Difference Equations, 2018 In this paper, we establish some relations involving q-Euler type sums, q-harmonic numbers and q-polylogarithms. Then, using the relations obtained with the help of q-analog of partial fraction decomposition formula, we develop new closed form ...
Xin Si
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On some series involving harmonic and skew-harmonic numbers
Journal of Classical Analysis, 2023 In this paper, we evaluate in closed form several different series involving the harmonic numbers and skew-harmonic numbers. We consider two classes of series involving these sequences. One class of series involves the product of the $n$th harmonic or skew-harmonic number and a tail.
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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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Axioms, 2022 In this paper, we focus on the higher-order derivatives of the hyperharmonic polynomials, which are a generalization of the ordinary harmonic numbers. We determine the hyperharmonic polynomials and their successive derivatives in terms of the r-Stirling ...
José L. Cereceda
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