Results 271 to 280 of about 11,829,477 (307)

Quadratic harmonic number sums

2012
After having recalled the sums involving harmonic numbers \(H_n =\sum_{j=1}^n j^{-1}\) (studied, e.g., by \textit{M. Hassani} [Int. J. Math. Combin. 2, 78--86 (2008; Zbl 1188.65002)] and by \textit{A. Sofo} [J. Appl. Anal. 16, No. 2, 265--277 (2010; Zbl 1276.11028)]), the authors clarify that their main result consists of new identities for the series \
Sofo, Anthony, Hassani, Mehdi
openaire   +1 more source

Dynamic Model and Analysis of Three phase YD Transformer Based Dual Active Bridge Using Optimised Harmonic Number for Solid State Transformer in Distributed System

2018 IEEE Innovative Smart Grid Technologies - Asia (ISGT Asia), 2018
M. T. Iqbal, A. I. Maswood, Kevin Yeo, M. Tariq   +3 more
semanticscholar   +1 more source

Harmonic Numbers of Any Order and the Wolstenholme’s-Type Relations for Harmonic Numbers

2016
The concept of harmonic numbers has appeared permanently in the mathematical science since the very early days of differential and integral calculus. Firsts significant identities concerning the harmonic numbers have been developed by Euler (see Basu, Ramanujan J, 16:7–24, 2008, [1], Borwein and Bradley, Int J Number Theory, 2:65–103, 2006, [2], Sofo ...
Edyta Hetmaniok, Piotr Lorenc, Mariusz Pleszczyński, Michał Różański, Marcin Szweda, Roman Wituła   +5 more
openaire   +1 more source

Combinatorial identities on \(q\)-harmonic numbers

2011
Summary: By means of the \(q\)-finite differences and the derivative operator, we derive, from an alternating \(q\)-binomial sum identity with a free variable \(x\), several interesting identities concerning the generalized \(q\)-harmonic numbers.
CHU, Wenchang, YAN Q.
openaire   +2 more sources

Harmonic number identities involving telescoping method and derivative operator

, 2017
Qinglun Yan, Yaqing Liu
semanticscholar   +1 more source

Ramanujan’s Harmonic Number Expansion and Two Identities for Bernoulli Numbers

, 2017
A. Xu
semanticscholar   +1 more source

How to optimize high-order harmonic generation in gases

Nature Reviews Physics, 2022
Robin Weissenbilder, Laura Rego, Chen Guo   +2 more
exaly  

Quadratic and cubic harmonic number sums

, 2017
Xin Si, Ce Xu, Mingyu Zhang
semanticscholar   +1 more source

Modeling of a Li-ion battery energy storage system using an optimal harmonic number based model of DC-DC converter for more electric aircraft

Annual Conference of the IEEE Industrial Electronics Society, 2016
M. Tariq, A. I. Maswood, C. Gajanayake, A. Gupta   +3 more
semanticscholar   +1 more source

Riordan Array Approach to the Coefficients of Ramanujan’s Harmonic Number Expansion

, 2017
Lei Feng, Weiping Wang
semanticscholar   +1 more source