Abstract:
Relation between linear second order equations being confluent Heun equations: biconfluent and triconfluent – and first order linear systems of equations which generate Painlevë equations is studied. The generation process is interpreted in physical terms as antiquantization.Technically the study includes manipulations with polynomials. The complexity of computations sometimes demands the use of Algebraic Computing Systems.
Key words and phrases:antiquantization, Heun class equation, confluent Heun class equations, Painlevé equations, isomonodromy property, apparent singularities.