hyperharmonic numbers
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Author(s):  
Rusen Li

In this paper, we give explicit asymptotic formulas for some sums over primes involving generalized alternating hyperharmonic numbers of types I, II and III. Analogous results for numbers with $k$-prime factors will also be considered.


Author(s):  
Levent Kargın ◽  
Mümün Can ◽  
Ayhan Dil ◽  
Mehmet Cenkci

2021 ◽  
Vol 27 (2) ◽  
pp. 101-110
Author(s):  
José Luis Cereceda

In this paper, we obtain a new formula for the sums of k-th powers of the first n positive integers, Sk(n), that involves the hyperharmonic numbers and the Stirling numbers of the second kind. Then, using an explicit representation for the hyperharmonic numbers, we generalize this formula to the sums of powers of an arbitrary arithmetic progression. Furthermore, we express the Bernoulli polynomials in terms of hyperharmonic polynomials and Stirling numbers of the second kind. Finally, we extend the obtained formula for Sk(n) to negative values of n.


Author(s):  
Ayhan Dil ◽  
Erkan Muniroğlu

In this study, depending on the upper and the lower indices of the hyperharmonic number h(r), nonlinear recurrence relations are obtained. It is shown that generalized harmonic numbers and hyperharmonic numbers can be obtained from derivatives of the binomial coefficients. Taking into account of difference and derivative operators, several identities of the harmonic and hyperharmonic numbers are given. Negative-ordered hyperharmonic numbers are defined and their alternative representations are given.


2018 ◽  
Vol 11 (03) ◽  
pp. 1850045
Author(s):  
Neşe Ömür ◽  
Sibel Koparal

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]. We give some new factorizations and determinants of the matrices [Formula: see text] and [Formula: see text].


2017 ◽  
Vol 154 (1) ◽  
pp. 147-186 ◽  
Author(s):  
H. Göral ◽  
D. C. Sertbaş

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