Euler sums of generalized alternating hyperharmonic numbers

2021 ◽  
Vol 51 (4) ◽  
Author(s):  
Rusen Li
Keyword(s):  
Euler Sums ◽  
Hyperharmonic Numbers

scholarly journals Euler sums of hyperharmonic numbers

2015 ◽  
Vol 147 ◽  
pp. 490-498 ◽  
Author(s):  
Ayhan Dil ◽  
Khristo N. Boyadzhiev
Keyword(s):  
Euler Sums ◽  
Hyperharmonic Numbers

scholarly journals Sums of powers of integers and hyperharmonic numbers

2021 ◽  
Vol 27 (2) ◽  
pp. 101-110
Author(s):  
José Luis Cereceda
Keyword(s):  
Arithmetic Progression ◽  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Explicit Representation ◽  
Sums Of Powers ◽  
Hyperharmonic Numbers ◽  
New Formula ◽  
Positive Integers

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.

scholarly journals Euler sums and non-integerness of harmonic type sums

2019 ◽  
pp. 1-13
Author(s):  
Haydar Göral ◽  
Doğa Can Sertbaş
Keyword(s):  
Euler Sums

scholarly journals POLYLOGARITHMIC CONNECTIONS WITH EULER SUMS

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
ANTHONY SOFO
Keyword(s):  
Euler Sums

scholarly journals General order Euler sums with multiple argument

2018 ◽  
Vol 189 ◽  
pp. 255-271 ◽  
Author(s):  
Anthony Sofo
Keyword(s):  
Euler Sums ◽  
General Order
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