Results 41 to 50 of about 11,335,757 (341)
Approximations of the Harmonic Numbers
Results in MathematicsAbstract The aim of this paper is to present some approximations on the harmonic numbers. Some associated asymptotic series are constructed.
Chao-Ping Chen, Cristinel Mortici
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AppliedMathTwo 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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Evaluation of the real parts of polylogarithm expressions containing complex arguments via certain logarithmic integrals [PDF]
Notes on Number Theory and Discrete MathematicsWe 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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Telescoping method, derivative operators and harmonic number identities [PDF]
, 2012 In terms of the telescoping method, a simple binomial sum is given. By applying the derivative operators to the equation just mentioned, we establish several general harmonic number identities including some known results.
Chuanan Wei, Dianxuan Gong, Qinglun Yan
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Linear non-normal energy amplification of harmonic and stochastic forcing in turbulent channel flow [PDF]
, 2010 The linear response to stochastic and optimal harmonic forcing of small coherent perturbations to the turbulent channel mean flow is computed for Reynolds numbers ranging from Re_tau=500 to Re_tau=20000.
Hwang, Yongyun +3 more
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Multiple Argument Euler Sum Identities
MathematicsWe develop a number of new identities for linear Euler harmonic number sums with multiple argument. Some new examples of even weight linear Euler harmonic sum identities are given.
Anthony Sofo
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Harmonic dependence of thermal magnetic particle imaging
Scientific Reports, 2023 Advances in instrumentation and tracer materials are still required to enable sensitive, accurate, and localized in situ 3D temperature monitoring by magnetic particle imaging (MPI).
Thinh Q. Bui +4 more
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Pediatric gastroenteropancreatic neuroendocrine neoplasms (GEP‐NENs) are extremely rare and clinically heterogeneous. Management has largely been extrapolated from adult practice. This European Standard Clinical Practice Guideline (ESCP), developed by the EXPeRT network in collaboration with adult NEN experts, provides (adult) evidence ...
Michaela Kuhlen +23 more
wiley +1 more source
The monotonicity and convexity of a function involving psi function with applications
Journal of Inequalities and Applications, 2016 In this paper, we prove that the function x ↦ exp ( ψ ( x + 1 2 ) − 1 24 1 x 2 + 7 / 40 ) − x $$ x\mapsto\exp \biggl( \psi \biggl( x+\frac{1}{2} \biggr) -\frac {1}{24} \frac{1}{x^{2}+7/40} \biggr) -x $$ is decreasing from ( − 1 / 2 , ∞ ) $( -1/2,\infty )
Bang-Cheng Sun +3 more
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General Analytical Model of Magnet Average Eddy-Current Volume Losses for Comparison of Multi-phase PM Machines with Concentrated Winding [PDF]
, 2014 this paper studies magnet eddy-current losses in permanent magnet (PM) machines with concentrated winding. First of all, space harmonics of magnetomotive force (MMF) and their influence on magnet losses in electrical machines are investigated.
LEGRANGER, Jerome +2 more
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