Summation formulas involving generalized harmonic numbers

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 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

Summation formulas for Schur functions involving hyperdeterminants

We give general integral formulas involving for hyperdeterminants or hyperpfaffians. In the applications, we obtain several summation formulas for the products of Schur functions, which are generalizations of Cauchy’s determinant. Further, we study Toeplitz hyperdeterminants by using the theory of Jack polynomials and give a hyperdeterminant version of a strong Szegö limit theorem. MSC-class: p...

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...