Results 11 to 20 of about 11,335,757 (341)
Harmonic sets and the harmonic prime number theorem
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.
Broughan, Kevin A., Casey, Rory J.
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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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On the harmonic and hyperharmonic Fibonacci numbers [PDF]
Advances in Difference Equations, 2015 In this paper, we study the theory of the harmonic and the hyperharmonic Fibonacci numbers. Also, we get some combinatoric identities like as harmonic and hyperharmonic numbers and we obtain some useful formulas for $\mathbb{F}_{n}$, which is finite sums of reciprocals of Fibonacci numbers.
KESİM, SEYHUN +2 more
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ON THE CONVERGENCE OF THE EULER HARMONIC SERIES [PDF]
, 2000 The aim oj this article is to study the convergence oj the Euler harmonic series. Firstly, the results concerning the convergence oj the Smaralldache and Erdos harmonic junctions are reviewed Secondly, the Euler harmonic series is proved to be convergent
Tabirca, Tatiana, Tabirca, Sabin
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The sum of the telescoping series formed by reciprocals of the cubic polynomials with three different negative integer roots [PDF]
Mathematics in Education, Research and Applications, 2020 This paper deals with the sum of a special telescoping series and is a free follow-up to author’s preceding paper. The terms of this series are reciprocals of the cubic polynomial with three different negative integer roots.
Radovan Potůček
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Spatiotemporal phase-matching in capillary high-harmonic generation [PDF]
, 2012 We present a simple phase-matching model that takes into account the full spatiotemporal nature of capillary high-harmonic generation. Spectra predicted from the model are compared to experimental results for a number of gases and are shown to reproduce ...
Rogers, Edward T.F. +22 more
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Sharp bounds for harmonic numbers [PDF]
Applied Mathematics and Computation, 2011 7 ...
Bai-Ni Guo, Feng Qi 0001
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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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Riordan arrays and harmonic number identities
Computers and Mathematics with Applications, 2010 Let the numbers P(r,n,k) be defined by P(r,n,k):=Pr(Hn(1)−Hk(1),…,Hn(r)−Hk(r)), where Pr(x1,…,xr)=(−1)rYr(−0!x1,−1!x2,…,−(r−1)!xr) and Yr are the exponential complete Bell polynomials.
Weiping Wang
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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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