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Harmonic sets and the harmonic prime number theorem [PDF]
Bulletin of the Australian Mathematical Society, 2005 We restrict primes and prime powers to sets . Let . Then the error in θH(x) has, unconditionally, the expected order of magnitude . However, if then ψH (x) = x log 2 + O (log x). Some reasons for and consequences of these sharp results are explored. A proof is given of the “harmonic prime number theorem”, πH (x)/π (x) → log 2.
Kevin Broughan, Rory J. Casey
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Polynomials Related to Harmonic Numbers and Evaluation of Harmonic Number Series I [PDF]
Applicable Analysis and Discrete Mathematics, 2009 In this paper we focus on r-geometric polynomials, r-exponential polynomials and their harmonic versions. It is shown that harmonic versions of these polynomials and their generalizations are useful to obtain closed forms of some series related to harmonic numbers. 2000 Mathematics Subject Classification. 11B73, 11B75, 11B83.
Ayhan Dil, Veli Kurt
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AppliedMathBased on a recent representation of the psi function due to Guillera and Sondow and independently Boyadzhiev, new closed forms for various series involving harmonic numbers and inverse factorials are derived.
Kunle Adegoke, Robert Frontczak
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On the number of harmonic frames
Applied and Computational Harmonic Analysis, 2018 There is a finite number $h_{n,d}$ of tight frames of $n$ distinct vectors for $\mathbb{C}^d$ which are the orbit of a vector under a unitary action of the cyclic group $\mathbb{Z}_n$. These cyclic harmonic frames (or geometrically uniform tight frames) are used in signal analysis and quantum information theory, and provide many tight frames of ...
Simon Marshall, Shayne Waldron
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Hypergeometric Series and Harmonic Number Identities
Advances in Applied Mathematics, 2004 10 ...
Wenchang Chu, Livia De Donno
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rf acceleration with harmonic number jump [PDF]
Physical Review Special Topics. Accelerators and Beams, 2006 We have recently considered acceleration of protons and heavy ions in a fixed-field alternating-gradient accelerator with nonscaling lattice and linear field profile.
Alessandro G. Ruggiero
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On the number of nodal domains of spherical harmonics [PDF]
Topology, 1996 It is well known that the \(n\)-th eigenfunction to one-dimensional Sturm-Liouville eigenvalue problems has exactly \(n - 1\) nodes, i.e. non-degenerate zeros. For higher dimensions, it is much more complicated to obtain general statements on the zeros of eigenfunctions.
Josef Leydold
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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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Harmonic resolution as a holographic quantum number [PDF]
Journal of High Energy Physics, 2004 19 ...
Raphael Bousso
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The Harmonic Pitching NACA 0018 Airfoil in Low Reynolds Number Flow
EnergiesThis study investigates the aerodynamic performance of a symmetric NACA 0018 airfoil under harmonic pitching motions at low Reynolds numbers, a regime characterized by the presence of laminar separation bubbles and their impact on aerodynamic forces. The
Jan Michna +2 more
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