Summation formulae involving harmonic numbers

Abstract

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

Integrals of logarithmic and hypergeometric functions

“…Some results for sums of alternating harmonic numbers may be seen in the works [1], [2], [5], [6], [7], [9], [10], [12], [15], [16], [17], [20], [21], [19], [22], [23], [27], [28], [29] and [30] and references therein.…”

A family of shifted harmonic sums

“…Further work in the summation of harmonic numbers and binomial coefficients has been done by Sofo [20]. The works presented in (for example) [3,7,8,10,12,16,17,19,21,23,25,27,29,30] (see also [2,9] as well as the references cited in these works) investigate various closed-form representations of binomial sums and zeta functions by the use of the Beta function and by means of certain summation theorems for hypergeometric series.…”

Identities for Alternating Inverse Squared Binomial and Harmonic Number Sums

“…Chu [6] also proves many identities for finite sums of harmonic numbers and binomial coefficients, including, for example, .…”