  We perform a detailed study of a class of irregular correlators in Liouville
Conformal Field Theory, of the related Virasoro conformal blocks with irregular
singularities and of their connection formulae. Upon considering their
semi-classical limit, we provide explicit expressions of the connection
matrices for the Heun function and a class of its confluences. Their
calculation is reduced to concrete combinatorial formulae from conformal block
expansions.
