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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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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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Proceedings - Mathematical Sciences, 2021 The harmonic sums \(\sum_{r=k+1}^n \frac{1}{r}\) are not integers for any \(k \geq 1\). One way of proving this uses the Bertrand postulate that there is always a prime strictly between \(k\) and \(2k\) if \(k \geq 2\). The paper under review considers the more general analogous sums \(h_K(n) := \sum_{r=1}^n \frac{a_r}{r}\) where \(a_r\) is the number ...
Çağatay Altuntaş, Haydar Göral
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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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Application of Genetic Algorithm to Minimize Harmonic in Multilevel Inverter
Jurnal Nasional Teknik Elektro, 2016 In inverter design, harmonic voltage is the main issue which affects the performance of the inverter. Generally, the harmonic minimization problem complexity is influenced by the number of harmonic orders to be minimized.
Firmansyah Nur Budiman1 +2 more
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The Sum of the Series of Reciprocals of the Quadratic Polynomials with Complex Conjugate Roots
Ratio Mathematica, 2018 This contribution is a follow-up to author’s papers [1], [2], [3], [4], [5], [6], [7], and in particular [8] dealing with the sums of the series of reciprocals of quadratic polynomials with different positive integer roots, with double non-positive ...
Radovan Potucek
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Odd Euler Sums and Harmonic Series with Cubic Central Binomial Coefficients in Denominators
AxiomsBy means of the coefficient extraction method, we examine a transformation of a classical hypergeometric series. Three classes of infinite series (of convergence rate “1/4”) with harmonic numbers in numerators and cubic central binomial coefficients in ...
Chunli Li, Wenchang Chu
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Gauss’ Second Theorem for
MathematicsTwo summation theorems concerning the F12(1/2)-series due to Gauss and Bailey will be examined by employing the “coefficient extraction method”. Forty infinite series concerning harmonic numbers and binomial/multinomial coefficients will be evaluated in ...
Chunli Li, Wenchang Chu
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Summation Formulas Involving Binomial Coefficients, Harmonic Numbers, and Generalized Harmonic Numbers [PDF]
Abstract and Applied Analysis, 2014 A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and 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.
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