Results 51 to 60 of about 95 (80)

A symmetric algorithm for hyperharmonic and Fibonacci numbers [PDF]

Applied Mathematics and Computation, 2008
In this work, we introduce a symmetric algorithm obtained by the recurrence relation a_{n}^{k}=a_{n-1}^{k}+a_{n}^{k-1}. We point out that this algorithm can be apply to hyperharmonic-, ordinary and incomplete Fibonacci- and Lucas numbers. An explicit formulae for hyperharmonic numbers, general generating functions of the Fibonacci- and Lucas numbers ...
István Mező, Ayhan Dil
exaly   +4 more sources

Euler sums of generalized hyperharmonic numbers

Functiones Et Approximatio, Commentarii Mathematici, 2022
In this paper, we mainly show that Euler sums of generalized hyperharmonic numbers can be expressed in terms of linear combinations of the classical Euler sums.
Rusen Li
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Euler sums of multiple hyperharmonic numbers

Lithuanian Mathematical Journal, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ce Xu
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Divisibility properties of hyperharmonic numbers

Acta Mathematica Hungarica, 2017
The \(n\)th hyperharmonic number of order \(r\) is defined recursively by \(h_n^{(r)}=\sum_{k=1}^n h_k^{(r-1)}\), where \(h_n^{(1)}=\sum_{k=1}^n k^{-1}\) is the \(n\)th harmonic number. The authors prove a series of results for hyperharmonic numbers in this long paper.
Goral, H., Sertbas, D. C.
exaly   +3 more sources

Some Identities with Multi-Generalized q-Hyperharmonic Numbers of Order r

Symmetry, 2023
The main purpose of this paper is to define multiple alternative q-harmonic numbers, Hnk;q and multi-generalized q-hyperharmonic numbers of order r, Hnrk;q by using q-multiple zeta star values (q-MZSVs). We obtain some finite sum identities and give some applications of them for certain combinations of q-multiple polylogarithms Liq;k1,k2,…,kdt1,t2,…,td
Sibel Koparal, Waseem A. Khan, Zhihua Chen   +2 more
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A $$q$$ -analog of the hyperharmonic numbers

Afrika Matematika, 2012
After having recalled the harmonic numbers \(H(n)\) studied by \textit{J. M. Santmyer} [Discrete Math. 171, No. 1--3, 229--235 (1997; Zbl 0873.05006)], the \(r\)-order hyperharmonic numbers \(H(n,r)\) described by \textit{J. H. Conway} and \textit{R. K. Guy} [The book of numbers.
Mansour, Toufik, Shattuck, Mark
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A new generalization of hyperharmonic numbers

Annales Polonici Mathematici, 2022
Summary: A new generalization of hyperharmonic numbers, called degenerate hyperharmonic numbers, is introduced. Also, several combinatorial identities and summation formulas involving these numbers and some other special degenerate numbers such as higher-order degenerate Daehee numbers and degenerate derangement numbers are deduced by applying the ...
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Combinatorial identities involving degenerate harmonic and hyperharmonic numbers

Advances in Applied Mathematics, 2023
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Taekyun Kim 0001, Dae San Kim
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On the matrices with the generalized hyperharmonic numbers of order r

Asian-European Journal of Mathematics, 2018
In this paper, we define two [Formula: see text] matrices [Formula: see text] and [Formula: see text] with [Formula: see text] and [Formula: see text] respectively, where [Formula: see text] are a generalized hyperharmonic numbers of order [Formula: see text].
KOPARAL, SİBEL, ÖMÜR, NEŞE
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An introduction to hyperharmonic numbers

International Journal of Mathematical Education in Science and Technology, 2014
In this note, we deal with a generalization of the harmonic numbers proposed by Conway and Guy in their Book of Numbers, namely, the so-called hyperharmonic numbers. Our main aim is to prove, by mathematical induction, the formula defining the hyperharmonic numbers in terms of ordinary harmonic numbers.
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