Results 31 to 40 of about 351,945 (274)

Sharp bounds for harmonic numbers

, 2010
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 ...
Alzer, Alzer, Bai-Ni Guo, Batir, Chen, Chen, DeTemple, Feng Qi, Guo, Havil, High, Klambauer, Koumandos, Kuang, Kuang, Kuang, Pólya, Qi, Tóth, Tóth, Wei, Wu, Yang, Young   +23 more
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Some harmonic aggregation operators for N-valued neutrosophic trapezoidal numbers and their application to multi-criteria decision-making [PDF]

Neutrosophic Sets and Systems
As an extension of the both trapezoidal fuzzy numbers and neutrosophic trapezoidal numbers, the N-valued neutrosophic trapezoidal numbers, which are special neutrosophic multi-sets on subset of real numbers. Harmonic mean is a conservative average, which
İrfan DELİ , Vakkas ULUÇAY
doaj   +1 more source

Two problems of binomial sums involving harmonic numbers

Advances in Difference Equations, 2021
Two open problems recently proposed by Xi and Luo (Adv. Differ. Equ. 2021:38, 2021) are resolved by evaluating explicitly three binomial sums involving harmonic numbers, that are realized mainly by utilizing the generating function method and symmetric ...
Nadia N. Li, Wenchang Chu
doaj   +1 more source

Some Families of Apéry-Like Fibonacci and Lucas Series

Mathematics, 2021
In this paper, the authors investigate two special families of series involving the reciprocal central binomial coefficients and Lucas numbers. Connections with several familiar sums representing the integer-valued Riemann zeta function are also pointed ...
Robert Frontczak, Hari Mohan Srivastava, Živorad Tomovski   +2 more
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New Harmonic Number Series

AppliedMath
Based 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. A high point of the presentation is the rediscovery, by much simpler means, of a famous quadratic Euler sum originally discovered in 1995 by ...
Kunle Adegoke, Robert Frontczak
openaire   +3 more sources

Series involving degenerate harmonic numbers and degenerate Stirling numbers

Applied Mathematics in Science and Engineering
Recently, degenerate harmonic numbers and degenerate hyperharmonic numbers are introduced by Kim-Kim. In this paper, we study the series involving the degenerate harmonic numbers and degenerate Stirling numbers and investigate those properties.
Lingling Luo, Yuankui Ma, Taekyun Kim, Rongrong Xu   +3 more
doaj   +1 more source

Dirichlet series and series with Stirling numbers

Cubo, 2023
This paper presents a number of identities for Dirichlet series and series with Stirling numbers of the first kind. As coefficients for the Dirichlet series we use Cauchy numbers of the first and second kinds, hyperharmonic numbers, derangement numbers ...
Khristo Boyadzhiev
doaj   +1 more source

Binomial transform and the backward difference

, 2017
We prove an important property of the binomial transform: it converts multiplication by the discrete variable into a certain difference operator. We also consider the case of dividing by the discrete variable.
Boyadzhiev, Khristo N.
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Unified description of magic numbers of metal clusters in terms of the 3-dimensional q-deformed harmonic oscillator

, 2001
Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3)>SOq(3) symmetry are compared to experimental data for atomic clusters of alkali metals (Li, Na, K, Rb, Cs), noble metals (Cu, Ag, Au), divalent metals (Zn, Cd), and ...
A. A. Malashin, A. A. Malashin, A. Bulgac, A. J. Macfarlane, A. Klimyk, B. A. Kotsos, B. A. Kotsos, C. Bréchignac, D. Bonatsos, D. Bonatsos, D. Bonatsos, D. Bonatsos, D. Bonatsos, D. E. Beck, D. E. Beck, D. Lenis, Dennis Bonatsos, E. Koch, G. Alameddin, G. S. Anagnostatos, H. Fiedeldey, H. Göhlich, H. Nishioka, I. Katakuse, I. Katakuse, J. L. Persson, J. Pedersen, J. Van der Jeugt, J. Van der Jeugt, J. Van der Jeugt, K. Chadan, K. Clemenger, L. C. Biedenharn, M. B. Knickelbein, M. Brack, M. G. Mayer, N. D. Bhaskar, N. Karoussos, P. A. Terziev, P. P. Raychev, P. P. Raychev, R. P. Roussev, R. S. Mackintosh, R. S. Mackintosh, S. Bjørnholm, S. Bjørnholm, S. G. Nilsson, S. G. Nilsson, T. Bergmann, T. P. Martin, T. P. Martin, V. Chari, V. N. Ostrovsky, V. O. Nesterenko, V. Spiridonov, W. A. de Heer, W. A. de Heer, W. D. Knight, W. D. Knight, W. Ekardt, W. Ekardt, Yu. F. Smirnov, Yu. F. Smirnov, Yu. F. Smirnov   +63 more
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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.
openaire   +1 more source