scholarly journals Integrals of polylogarithms and infinite series involving generalized harmonic numbers

2021 ◽  
pp. 1-14
Author(s):  
Rusen Li
Keyword(s):  
Infinite Series ◽  
Harmonic Numbers ◽  
Generalized Harmonic Numbers

Binomial sums involving harmonic numbers

2011 ◽  
Vol 61 (2) ◽  
Author(s):  
Marian Genčev
Keyword(s):  
Infinite Series ◽  
Rational Functions ◽  
Harmonic Numbers ◽  
Binomial Type ◽  
Hypergeometric Type ◽  
Number Π ◽  
Binomial Sums ◽  
Generalized Harmonic Numbers

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.

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 On some combinatorial identities and harmonic sums

2017 ◽  
Vol 13 (07) ◽  
pp. 1695-1709 ◽  
Author(s):  
Necdet Batir
Keyword(s):  
Integral Representation ◽  
Closed Form ◽  
Generating Function ◽  
Combinatorial Identities ◽  
Harmonic Numbers ◽  
Generalized Harmonic Numbers

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.

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