Confluent Heun equation with single added apparent singularity

摘要

Elementary, gauge and Laplace integral symmetries of confluent Heun equation with single added apparent singularity are under consideration. Symmetries from this collection connect solutions of the same equation with different set of parameters. The derivation of these symmetries is based on usage of corresponding generating systems of the first-order equations, whose reduction to the scalar equation coincides with confluent Heun equation with single added apparent singularity. These symmetries can be expressed in terms of the monodromy group of this equation.