  We consider nested sums involving the Pochhammer symbol at infinity and
rewrite them in terms of a small set of constants, such as powers of $\pi,$
$\log(2)$ or zeta values. In order to perform these simplifications, we view
the series as specializations of generating series. For these generating
series, we derive integral representations in terms of root-valued iterated
integrals or directly in terms of cyclotomic harmonic polylogarithms. Using
substitutions, we express the root-valued iterated integrals as cyclotomic
harmonic polylogarithms. Finally, by applying known relations among the
cyclotomic harmonic polylogarithms, we derive expressions in terms of several
constants. The methods are implemented in the computer algebra package
HarmonicSums.
