On 3-adic Valuations of Generalized Harmonic Numbers

Integers ◽  
2012 ◽  
Vol 12 (2) ◽  
Author(s):  
Ken Kamano

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

2017 ◽  
Vol 13 (07) ◽  
pp. 1695-1709 ◽  
Author(s):  
Necdet Batir

For any [Formula: see text] we first give new proofs for the following well-known combinatorial identities [Formula: see text] and [Formula: see text] and then we produce the generating function and an integral representation for [Formula: see text]. Using them we evaluate many interesting finite and infinite harmonic sums in closed form. For example, we show that [Formula: see text] and [Formula: see text] where [Formula: see text] are generalized harmonic numbers defined below.


2020 ◽  
Vol 26 (4) ◽  
pp. 39-51
Author(s):  
Laid Elkhiri ◽  
◽  
Miloud Mihoubi ◽  
Abdellah Derbal ◽  
◽  
...  

In 2017, Bing He investigated arithmetic properties to obtain various basic congruences modulo a prime for several alternating sums involving harmonic numbers and binomial coefficients. In this paper we study how we can obtain more congruences modulo a power of a prime number p (super congruences) in the ring of p-integer \mathbb{Z}_{p} involving binomial coefficients and generalized harmonic numbers.


Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 577 ◽  
Author(s):  
Giuseppe Dattoli ◽  
Silvia Licciardi ◽  
Elio Sabia ◽  
Hari M. Srivastava

In this paper, we introduce higher-order harmonic numbers and derive their relevant properties and generating functions by using an umbral-type method. We discuss the link with recent works on the subject, and show that the combinations of umbral and other techniques (such as the Laplace and other types of integral transforms) yield a very efficient tool to explore the properties of these numbers.


2011 ◽  
Vol 61 (2) ◽  
Author(s):  
Marian Genčev

AbstractThis paper develops the approach to the evaluation of a class of infinite series that involve special products of binomial type, generalized harmonic numbers of order 1 and rational functions. We give new summation results for certain infinite series of non-hypergeometric type. New formulas for the number π are included.


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