Add to ORKGWe seek to discover combinatorial explanations of known identities involving harmonic numbers. Harmonic numbers do not readily lend themselves to combinatorial interpretation, since they are sums of fractions, and combinatorial arguments involve counting whole objects. It turns out that we can transform these harmonic identities into new identities involving Stirling numbers, which are much more apt to combinatorial interpretation. We have proved four of these identities, the first two being special cases of the third
In this paper, we study the properties of the generalized harmonic numbersHn,k,r(α, β). In particula...
There have been derivations for the Sums of Powers published since the sixteenth century. All techni...
AbstractThe authors developed closed-form sums of several interesting families of series associated ...
Hyperharmonic numbers arise by taking repeated partial sums of harmonic numbers. These numbers can b...
Hyperharmonic numbers arise by taking repeated partial sums of harmonic numbers. These numbers can b...
Hyperharmonic numbers arise by taking repeated partial sums of harmonic numbers. These numbers can b...
The master’s thesis discusses harmonic numbers These prove to be very useful in the field of number t...
AbstractIn this paper we consider five conjectured harmonic number identities similar to those arisi...
This book is a unique work which provides an in-depth exploration into the mathematical expertise, p...
AbstractLet the numbers P(r,n,k) be defined by P(r,n,k):=Pr(Hn(1)−Hk(1),…,Hn(r)−Hk(r)), where Pr(x1,...
In this paper, polynomials whose coefficients involve $r$-Lah numbers are used to evaluate several s...
AbstractTwo open problems recently proposed by Xi and Luo (Adv. Differ. Equ. 2021:38, 2021) are reso...
We present new proofs for some summation identities involving Stirling numbers of both first and sec...
Recently, McCarthy presented two algebraic identities involving binomial coefficients and harmonic n...
AbstractBy observing that the infinite triangle obtained from some generalized harmonic numbers foll...
In this paper, we study the properties of the generalized harmonic numbersHn,k,r(α, β). In particula...
There have been derivations for the Sums of Powers published since the sixteenth century. All techni...
AbstractThe authors developed closed-form sums of several interesting families of series associated ...
Hyperharmonic numbers arise by taking repeated partial sums of harmonic numbers. These numbers can b...
Hyperharmonic numbers arise by taking repeated partial sums of harmonic numbers. These numbers can b...
Hyperharmonic numbers arise by taking repeated partial sums of harmonic numbers. These numbers can b...
The master’s thesis discusses harmonic numbers These prove to be very useful in the field of number t...
AbstractIn this paper we consider five conjectured harmonic number identities similar to those arisi...
This book is a unique work which provides an in-depth exploration into the mathematical expertise, p...
AbstractLet the numbers P(r,n,k) be defined by P(r,n,k):=Pr(Hn(1)−Hk(1),…,Hn(r)−Hk(r)), where Pr(x1,...
In this paper, polynomials whose coefficients involve $r$-Lah numbers are used to evaluate several s...
AbstractTwo open problems recently proposed by Xi and Luo (Adv. Differ. Equ. 2021:38, 2021) are reso...
We present new proofs for some summation identities involving Stirling numbers of both first and sec...
Recently, McCarthy presented two algebraic identities involving binomial coefficients and harmonic n...
AbstractBy observing that the infinite triangle obtained from some generalized harmonic numbers foll...
In this paper, we study the properties of the generalized harmonic numbersHn,k,r(α, β). In particula...
There have been derivations for the Sums of Powers published since the sixteenth century. All techni...
AbstractThe authors developed closed-form sums of several interesting families of series associated ...