Derivative operator and summation formulae involving generalized harmonic numbers

Summation formulae involving harmonic numbers

Several summation formulae for finite and infinite series involving the classical harmonic numbers are presented. The classical harmonic numbers are defined by

Some summation formulas involving harmonic numbers and generalized 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.

Identities Involving Generalized Harmonic Numbers and Other Special Combinatorial Sequences

In this paper, we study the properties of the generalized harmonic numbersHn,k,r(α, β). In particular, by means of the method of coefficients, generating functions and Riordan arrays, we establish some identities involving the numbers Hn,k,r(α, β), Cauchy numbers, generalized Stirling numbers, Genocchi numbers and higher order Bernoulli numbers. Furthermore, we obtain the asymptotic values of s...