Harmonic Numbers of Any Order and the Wolstenholme’s-Type Relations for Harmonic Numbers

2016 ◽  
pp. 33-44
Author(s):  
Edyta Hetmaniok ◽  
Piotr Lorenc ◽  
Mariusz Pleszczyński ◽  
Michał Różański ◽  
Marcin Szweda ◽  
...  
Keyword(s):  
Harmonic Numbers

On 3-adic Valuations of Generalized Harmonic Numbers

Integers ◽  
2012 ◽  
Vol 12 (2) ◽  
Author(s):  
Ken Kamano
Keyword(s):  
Harmonic Numbers ◽  
Generalized Harmonic Numbers

Abstract.We investigate 3-adic valuations of generalized harmonic numbers

scholarly journals Some combinatorial series identities associated with the Digamma function and harmonic numbers

2000 ◽  
Vol 13 (3) ◽  
pp. 101-106 ◽  
Author(s):  
Tsu-Chen Wu ◽  
Shih-Tong Tu ◽  
H.M. Srivastava
Keyword(s):  
Harmonic Numbers ◽  
Digamma Function

scholarly journals A Computer Proof of a Series Evaluation in Terms of Harmonic Numbers

2002 ◽  
Vol 13 (4) ◽  
pp. 327-333 ◽  
Author(s):  
Russell Lyons ◽  
Peter Paule ◽  
Axel Riese
Keyword(s):  
Harmonic Numbers ◽  
Series Evaluation ◽  
Computer Proof

scholarly journals Harmonic Numbers and Cubed Binomial Coefficients

2011 ◽  
Vol 2011 ◽  
pp. 1-14
Author(s):  
Anthony Sofo
Keyword(s):  
Closed Form ◽  
Binomial Coefficients ◽  
Harmonic Numbers ◽  
Polygamma Functions ◽  
Form Representation ◽  
The Given

Euler related results on the sum of the ratio of harmonic numbers and cubed binomial coefficients are investigated in this paper. Integral and closed-form representation of sums are developed in terms of zeta and polygamma functions. The given representations are new.

scholarly journals Sequences of Prime Reciprocals. Preliminaries

2018 ◽  
Vol 26 (1) ◽  
pp. 69-79
Author(s):  
Adam Grabowski
Keyword(s):  
Natural Number ◽  
Harmonic Numbers ◽  
Mizar Mathematical Library

Summary In the article we formalize some properties needed to prove that sequences of prime reciprocals are divergent. The aim is to show that the series exhibits log-log growth. We introduce some auxiliary notions as harmonic numbers, telescoping series, and prove some standard properties of logarithms and exponents absent in the Mizar Mathematical Library. At the end we proceed with square-free and square-containing parts of a natural number and reciprocals of corresponding products.

scholarly journals Sharp inequalities for the harmonic numbers

2012 ◽  
Vol 28 (2) ◽  
pp. 223-229
Author(s):  
CHAO-PING CHEN ◽  
Keyword(s):  
Harmonic Number ◽  
Harmonic Numbers ◽  
Double Inequality

Let Hn be the nth harmonic number, and let γ be the Euler-Mascheroni constant. We prove that for all integers n ≥ 1, the double-inequality ... holds with the best possible constants ... We also establish inequality for the Euler-Mascheroni constant.

On some congruences involving Domb numbers and harmonic numbers

2019 ◽  
Vol 15 (10) ◽  
pp. 2179-2200 ◽  
Author(s):  
Guo-Shuai Mao ◽  
Jie Wang
Keyword(s):  
Harmonic Numbers

In this paper, we prove three congruences involving Apéry-like numbers [Formula: see text] and [Formula: see text] which have been conjectured by Sun. These numbers are defined by [Formula: see text] [Formula: see text]

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