Symmetries of the confluent Heun equation

The group of the discrete symmetries of the confluent Heun equation is under consideration. This group has as generators the elementary symmetries and the integral symmetries. Such lead to the corresponding symmetries of the connection matrix, which describe the relations between the different fundamental sets of the solutions. The symmetry of the confluent Heun equation with respect to the integral Laplace transform leads to the corresponding relations between the Stokes parameters and connection matrix.