Summation formulae involving harmonic numbers

Finite summation formulas involving binomial coefficients, harmonic numbers and generalized harmonic numbers

A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics and theoretical physics. Here we show how one can obtain further interesting identities about certain fin...

Summation Formulae and Stirling Numbers

We exploit methods of operational and combinatorial nature to get a class of summation formulae involving special functions and polynomi-als. The results obtained in this paper complete and integrate previous investigations obtained with different methods.

Dixon’s Formula and Identities Involving Harmonic Numbers

Inspired by the recent work of Chu and Fu, we derive some new identities with harmonic numbers from Dixon’s hypergeometric summation formula by applying the derivation operator to the summation of binomial coefficients.

A Comment on Matiyasevich’s Identity #0102 with Bernoulli Numbers

We connect and generalize Matiyasevich’s identity #0102 with Bernoulli numbers and an identity of Candelpergher, Coppo and Delabaere on Ramanujan summation of the divergent series of the infinite sum of the harmonic numbers. The formulae are analytic continuation of Euler sums and lead to new recursion relations for derivatives of Bernoulli numbers. The techniques used are contour integration, ...

Some summation formulas involving harmonic numbers and generalized harmonic numbers