Related papers: Summation formulas involving generalized harmonic …

Combining the derivative operator with a binomial sum from the telescoping method, we establish a family of summation formulas involving generalized harmonic numbers.

Combining the derivative operator with Chu-Vandermonde convolution, we establish a class of summation formulas on generalized harmonic numbers.

In terms of the derivative operator, integral operator and Saalsch\"{u}tz's theorem, two families of summation formulae involving generalized harmonic numbers are established.

We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both…

By means of the derivative operator and Whipple-type $_3F_2$-series identities, two families of summation formulae involving generalized harmonic numbers are established.

In this paper, we give explicit evaluation for some infinite series involving generalized (alternating) harmonic numbers. In addition, some formulas for generalized (alternating) harmonic numbers will also be derived.

In terms of the derivative operator and Watson-type $_3F_2$-series identities, three families of summation formulae involving generalized harmonic numbers are established.

By some hypergeometric summation theorems, the authors establish a series of new infinite summation formulas involving generalized harmonic numbers related to Riemann-Zeta function, with three different patterns.

The classical hypergeometric summation theorems are exploited to derive several striking identities on harmonic numbers including those discovered recently by Paule and Schneider (2003).

In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals

Harmonic numbers are important in a lot of branches of number theory. By means of the derivative operator, the integral operator, and several summation and transformation formulas for hypergeometric series, we prove four series containing…

In this paper, we consider three families of numerical series with general terms containing the harmonic numbers, and we use simple methods from classical and complex analysis to find explicit formulas for their respective sums.

By means of the derivative operator and Chu-Vandermonde convolution, four families of summation formulas involving harmonic numbers with even or odd indexes are established.

We offer some summation formulas that appear to have great utility in probability theory. The proofs require some recent results from analysis that have thus far been applied to basic hypergeometric functions.

Several new identities for elliptic hypergeometric series are proved. Remarkably, some of these are elliptic analogues of identities for basic hypergeometric series that are balanced but not very-well-poised.

By employing certain extended classical summation theorems, several surprising \pi and other formulae are displayed.

We show how infinite series of a certain type involving generalized harmonic numbers can be computed using a knowledge of symmetric functions and multiple zeta values. In particular, we prove and generalize some identities recently…

Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…

We establish several summation formulae for hypergeometric and basic hypergeometric series involving noncommutative parameters and argument. These results were inspired by a recent paper of J. A. Tirao [Proc. Nat. Acad. Sci. 100 (14)…

In this paper, several weighted summation formulas of $q$-hyperharmonic numbers are derived. As special cases, several formulas of hyperharmonic numbers of type $\sum_{\ell=1}^{n} {\ell}^{p} H_{\ell}^{(r)}$ and $\sum_{\ell=0}^{n} {\ell}^{p}…