Abstract
We present an infinite series formula based on the Karoubi–Hamida integral, for the universal Borel class evaluated on
(GL(ℂ)). For a cyclotomic field
we define a canonical set of elements in
) and present a novel approach (based on a free differential calculus) to constructing them. Indeed, we are able to explicitly construct their images in
(GL(ℂ)) under the Hurewicz map. Applying our formula to these images yields a value
), which coincides with the Borel regulator
) when our set is a basis of
) modulo torsion. For
= ℚ(
) a computation of
) has been made based on our techniques.