  Classical Virasoro conformal blocks are believed to be directly related to
accessory parameters of Floquet type in the Heun equation and some of its
confluent versions. We extend this relation to another class of accessory
parameter functions that are defined by inverting all-order Bohr-Sommerfeld
periods for confluent and biconfluent Heun equation. The relevant conformal
blocks involve Nagoya irregular vertex operators of rank 1 and 2 and
conjecturally correspond to partition functions of a 4D $\mathcal{N}=2$,
$N_f=3$ gauge theory at strong coupling and an Argyres-Douglas theory.
