Results 11 to 20 of about 95 (80)
On q-generalized hyperharmonic numbers with two parameters [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we introduce q-generalized harmonic numbers with two parameters ω and ξ, H_{μ,λ,q}(ω,ξ) for integers μ, λ such that λ ≥ μ. With the help of these numbers, we define a new family of numbers which is called q-generalized hyperharmonic ...
Neşe Ömür, Sibel Koparal, Ömer Duran
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Some identities associated with degenerate harmonic and hyperharmonic numbers
Mathematical and Computer Modelling of Dynamical SystemsThe study of degenerate versions of special polynomials and numbers has seen significant progress in recent years. In this paper, we establish several identities involving degenerate harmonic and hyperharmonic numbers, which are degenerate versions of ...
Qixiang Wang +4 more
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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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Summation formulas of hyperharmonic numbers with their generalizations
Afrika Matematika, 2023 In 1990, Spieß\, gave some identities of harmonic numbers including the types of $\sum_{\ell=1}^n\ell^k H_\ell$, $\sum_{\ell=1}^n\ell^k H_{n-\ell}$ and $\sum_{\ell=1}^n\ell^k H_\ell H_{n-\ell}$. In this paper, we derive several formulas of hyperharmonic numbers including $\sum_{\ell=0}^{n} {\ell}^{p} h_{\ell}^{(r)} h_{n-\ell}^{(s)}$ and $\sum_{\ell=0 ...
Takao Komatsu, Rusen Li
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On sums with generalized harmonic, hyperharmonic and special numbers [PDF]
Miskolc Mathematical Notes, 2020 In this paper, we establish interesting sums including generalized harmonic numbers and special numbers by using generating functions of these numbers and some combinatorial identities.
Duran, Ö., Ömür, N., Koparal, S.
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Euler sums of hyperharmonic numbers
Journal of Number Theory, 2015 9 ...
Ayhan Dil, Khristo N. Boyadzhiev
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On identities involving generalized harmonic, hyperharmonic and special numbers with Riordan arrays
Special Matrices, 2021 In this paper, by means of the summation property to the Riordan array, we derive some identities involving generalized harmonic, hyperharmonic and special numbers.
Koparal Sibel, Ömür Neşe, Duran Ömer
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Some identities on degenerate hyperharmonic numbers
Georgian Mathematical Journal, 2022 Abstract The aim of this paper is to investigate some properties, recurrence relations and identities involving degenerate hyperharmonic numbers, hyperharmonic numbers and degenerate harmonic numbers. In particular, we derive an explicit expression of the degenerate hyperharmonic numbers in terms of the degenerate harmonic numbers.
Kim, Taekyun, Kim, Dae San
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Statistical Uncertainty in Hydrometeorological Trend Analyses
Advances in Meteorology, Volume 2016, Issue 1, 2016., 2016 This study demonstrates the existence of uncertainty in hydrometeorological trend analyses using historical rainfall from Kenya in East Africa. With respect to the influence of short‐ and long‐term persistence on trend analyses, a total of 13 approaches of rank‐based techniques including Mann‐Kendall, Spearman’s Rho, and Cumulative Rank Difference (CRD)
Charles Onyutha, Anthony R. Lupo
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On the bounds for the spectral norms of geometric circulant matrices
Journal of Inequalities and Applications, 2016 In this paper, we define a geometric circulant matrix whose entries are the generalized Fibonacci numbers and hyperharmonic Fibonacci numbers. Then we give upper and lower bounds for the spectral norms of these matrices.
Can Kızılateş, Naim Tuglu
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