Quadratic alternating harmonic number sums

Abstract

We develop new closed form representations of sums of quadratic alternating harmonic numbers and reciprocal binomial coefficients.

Harmonic Numbers at Half Integer and Binomial Squared Sums

“…It is possible to represent the alternating harmonic number sums (14), (15) and (16) in terms of an integral, this is developed in the next theorem.…”

Infinite series identities involving quadratic and cubic harmonic numbers

“…[3,5,17,21]). Sofo and Hassani [19] derived further formulae by logarithmic integrals. Recently, Abel's lemma on summation by parts has been modified by Chu [10] to derive several infinite series identities involving the classical harmonic numbers and their variants.…”

Some results on q-harmonic number sums

“…For instance, in [2], Sofo gave the following identity: 4) where ζ (p) stands for the classical Riemann zeta function defined by [3] ζ (p) :…”

“…There are many works investigating sums of both harmonic numbers and binomial coefficients (see, for example, [1,2,[4][5][6] and the references therein). which is just the classical Euler sums S m,p defined in [7], where m := (m 1 , m 2 , .…”