Affiliation:
1. Bomaderry NSW , Australia
Abstract
Abstract
In this paper a number of new explicit expressions for quadratic Euler-type sums containing double-index harmonic numbers H
2
n
are given. These are obtained using ordinary generating functions containing the square of the harmonic numbers H
n
. As a by-product of the generating function approach used new proofs for the remarkable quadratic series of Au-Yeung
∑
n
=
1
∞
(
H
n
n
)
2
=
17
π
4
360
\sum\limits_{n = 1}^\infty {{{\left( {{{{H_n}} \over n}} \right)}^2} = {{17{\pi ^4}} \over {360}}}
together with its closely related alternating cousin are given. New proofs for other closely related quadratic Euler-type sums that are known in the literature are also obtained.
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