Accessory parameters in confluent Heun equations and classical irregular conformal blocks

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