Summation formulae involving multiple 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

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.

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...

Supercongruences Involving Multiple Harmonic Sums and Bernoulli Numbers

In this paper, we study some supercongruences involving multiple harmonic sums by using Bernoulli numbers. Our main theorem generalizes previous results by many different authors and confirms a conjecture by the authors and their collaborators. In the proof, we will need not only the ordinary multiple harmonic sums in which the indices are ordered, but also some variant forms in which the indic...