Results 21 to 30 of about 640,777 (319)
Some summation formulas involving harmonic numbers and generalized harmonic numbers [PDF]
Mathematical and Computer Modelling, 2011 Harmonic numbers and generalized harmonic numbers have been studied since the distant past and are involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics and theoretical physics.
Junesang Choi, Hari M. Srivastava
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Algebraic Relations Between Harmonic Sums and Associated Quantities [PDF]
, 2003 We derive the algebraic relations of alternating and non-alternating finite harmonic sums up to the sums of depth~6. All relations for the sums up to weight~6 are given in explicit form.
Anastasiou +156 more
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Families of Integrals of Polylogarithmic Functions
Mathematics, 2019 We give an overview of the representation and many connections between integrals of products of polylogarithmic functions and Euler sums. We shall consider polylogarithmic functions with linear, quadratic, and trigonometric arguments, thereby producing ...
Anthony Sofo
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Sharp bounds for harmonic numbers [PDF]
Applied Mathematics and Computation, 2011 In the paper, we first survey some results on inequalities for bounding harmonic numbers or Euler-Mascheroni constant, and then we establish a new sharp double inequality for bounding harmonic numbers as follows: For $n\in\mathbb{N}$, the double inequality -\frac{1}{12n^2+{2(7-12 )}/{(2 -1)}}\le H(n)-\ln n-\frac1{2n}-
Bai-Ni Guo, Feng Qi
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Cubic harmonics and Bernoulli numbers [PDF]
Journal of Combinatorial Theory, Series A, 2012 18 pages, 3 ...
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Median Bernoulli Numbers and Ramanujan’s Harmonic Number Expansion
Mathematics, 2022 Ramanujan-type harmonic number expansion was given by many authors. Some of the most well-known are: Hn∼γ+logn−∑k=1∞Bkk·nk, where Bk is the Bernoulli numbers.
Kwang-Wu Chen
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Harmonic numbers, harmonic series and zeta function [PDF]
Moroccan Journal of Pure and Applied Analysis, 2018 AbstractThis 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. The other parts are devoted to the seriesis(z)=∑n=1∞μ(n)nszn$\mathcal{M}{i_s}(z) = \sum\limits_{
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Non-Uniform Time Sampling for Multiple-Frequency Harmonic Balance Computations [PDF]
, 2013 A time-domain harmonic balance method for the analysis of almost-periodic (multi-harmonics) flows is presented. This method relies on Fourier analysis to derive an efficient alternative to classical time marching schemes for such flows.
Dufour, Guillaume +5 more
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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 identity, etc.
Fatih Yılmaz +2 more
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New 5-Phase Concentrated Winding Machine with Bi-Harmonic Rotor for Automotive Application [PDF]
, 2014 For a power range from 10 to 30 kW, 5-phase machines are well adapted to low-voltage (48V) supply thanks to their reduced current per phase. For three-phase machines but with higher voltages (>120V), machines with a number of slots per pole and per phase
ASLAN, Bassel, SEMAIL, Eric
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