Results 21 to 30 of about 98,048 (175)

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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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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Effect of Viscous Energy Dissipation on Transient Laminar Free Convective Flow of a Dusty Viscous Fluid through a Porous Medium

Journal of Applied Sciences and Environmental Management, 2023
A study on transient free convection flow of a dusty viscous fluid through a porous medium is important for improving the existing industrial processes and for developing new chemical and geothermal systems.
O. R. Jimoh, I. Ibrahim
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Series associated with harmonic numbers, Fibonacci numbers and central binomial coefficients $binom{2n}{n}$ [PDF]

Notes on Number Theory and Discrete Mathematics
We find various series that involve the central binomial coefficients $binom{2n}{n}$, harmonic numbers and Fibonacci numbers. Contrary to the traditional hypergeometric function _pF_q approach, our method utilizes a straightforward transformation to ...
Segun Olofin Akerele, Olamide Esther Salami   +1 more
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Harmonic Current Estimation of Unmonitored Harmonic Sources With a Novel Oversampling Technique for Limited Datasets

IEEE Access, 2022
In modern power systems, harmonics are amongst the significant issues attributed to renewable energy sources and nonlinear loads. Direct harmonic monitoring of the entire power system may be too costly or impractical, and measured data could be limited ...
Ahmadreza Eslami, Michael Negnevitsky, Evan Franklin, Sarah Lyden   +3 more
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Evaluation of the real parts of polylogarithm expressions containing complex arguments via certain logarithmic integrals [PDF]

Notes on Number Theory and Discrete Mathematics
We consider a polylogarithm expression containing complex arguments, namely 𝓟±(n)=ℜ(Liₙ((1±i)/2)). The central notion of the present paper is to evaluate the real parts of 𝓟±(n) for first four orders, specifically n = 1,2,3, and 4, by constructing ...
Narendra Bhandari
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Some summation formulas involving harmonic numbers and generalized harmonic numbers

Mathematical and Computer Modelling, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Choi, Junesang, Srivastava, H. M.
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Evaluation of Harmonic Number Series Involving the Binomial Coefficient C(3n,n) in the Denominator by Integration

AppliedMath
Two classes of series involving differences of harmonic numbers and the binomial coefficients C(3n,n) are evaluated in closed form. The classes under consideration are ∑k=0∞H3k+1−Hk(3k+1)3kkkmzkand∑k=0∞H2k−Hk(3k+1)3kkkmzk, where z is a complex number and
Kunle Adegoke, Robert Frontczak
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Harmonic number identities via polynomials with r-Lah coefficients

Comptes Rendus. Mathématique, 2020
In this paper, polynomials whose coefficients involve $r$-Lah numbers are used to evaluate several summation formulae involving binomial coefficients, Stirling numbers, harmonic or hyperharmonic numbers.
Kargın, Levent, Can, Mümün
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